This is a honking mess if you really want to stick to some semblance of Real Life physics and physionomics1
Assuming for no reason other than convenience that you have two parents that come from two unrelated (or so distantly related they might as well be unrelated) families. Each parent brings that family's intrinsic frequency with them. Those intrinsic frequencies would be, for the purposes of this analysis, random. Let's stay sane and suggest that the genetic frequency spectrum is the FM-Radio spectrum. So parent A comes with, oh, 89Mhz and parent B comes with 102Mhz.
Problem #1: Neither parent can really communicate with each other. If they can, then just about everybody can communicate with each other. We've already violated the basic premise of your question.
Problem #2: The way genetics as we understand it works, Their children might broadcast on 89Mhz, or 102Mhz, or on a frequency one of the grandparents or an even more distant ancestor broadcast on, like 107Mhz. My point is, we're already throwing everything we know about how life works out the window just to make the premise of your question work. This is because the only thing "natural" about radio is the use of the electromagnetic spectrum.
So, while you want something "feasible" in terms of how radio works, we're already throwing out whatever might be "feasible" in terms of how life works. So asking if bio-radio is "feasible" isn't valuable as we pretty much need to ignore the biological foundation it would be built on just to get the result you're looking for.
So let's ignore that aspect of your question and simply invite the alternative question, "how could I use something that sounds like Real Life to explain my bio-radio behavior?"
That we can do!
Carrier Frequencies, Modulation and Notch Filters
Over-simplifying radio to the point that angels weep, radio is comprised of carrier frequencies, modulation, and notch filters.
A Carrier Frequency is the frequency you tune you radio to. If your favorite radio station is on 94.8Mhz, that's the carrier frequency. In your world, once your progenitor or progenitors become established as a "family," there is a single carrier frequency. There's something2 pre-procreation that shifts the carrier frequency a child received from their parents just a little bit.3 This is important so that directly-related but distant relations can't talk to one another. So the further out vertically in the family tree you are, the harder it is to hear someone. (It's important to integrate a very minute shift of carrier frequency for each child. Close enough so that during the majority of their life it can be said they all have the same carrier frequency. You'll see why below.)
Modulation is the imposition of one signal onto the carrier frequency. If you don't know what that means, draw yourself a big, wide sine-wave on a piece of paper. Now trace over it, but as you do, wiggle the pencil up and down. Congratulations! You just learned how radio basically works. You "tune in" to the carrier frequency, then extract it. The result is the signal superimposed on it. Personally, I think the signal you just extracted from the carrier wave (called demodulation) is Johnny Rivers' Rockin' Pneumonia. Yeah, Baby! Why is modulation important? Because how something is modulated matters. There are different methods. Don't worry about what they are! There's no way on the planet that biological modulation can work the way radio modulation does. But a chromosomal-based modulation is something I think hits suspension-of-disbelief. The specific mix of chromosomes sets the modulation. Because the chromosomal mix between siblings is close, they can hear each other clearly. But it separates with the introduction of new chromosomes. Which means cousins have trouble hearing each other. And the further out horizontally in the family tree you are, the harder it is to hear someone.4
A notch filter is one of a number of methods of blocking signals from carrier waves you don't want to deal with. Demodulating multiple carrier waves is a nightmare. Think about trying to listen to multiple radio stations all at once, clear as a bell. It's not like trying to have a conversation in a crowded room because that noise decreases with distance. Multiple radio stations don't. Yeah. Bad. In Real Life notch filters aren't perfect which is why stations are allowed to operate only at specific, intentionally separated frequencies.5 But the basic premise of a notch filter is that all signals from frequencies outside of the notch can't be heard. This is your aging modifier. As a person ages, the notch gets narrower. Remember when I said each sibling had a unique carrier frequency that was a minute shift from, let's call it... "true center?" If the individual gets old enough, the notch filter grows so narrow that they can't hear anybody. They become "telepathically" deaf. But this isn't all!!! The cool thing about a notch filter is that you can have individuals born with a "disorder." They're notch filter is unusually wide, which means they can hear other transmissions with the same problems we would have trying to listen to multiple radio stations simultaneously. Such people may never grow out of this and would, perhaps, be maddened all their lives. Others might have a naturally narrowing notch filter that would allow them to hear their siblings in old age.
That was ugly... summary time!
Children have a carrier frequency that's a minor shift from the parent's carrier frequency. It's inside the notch filter. These slight shifts eventually fall outside the carrier-frequency-centered notch filter of ancestors, prohibiting communication after too many generations (forward or backward).
Children have a chromosome-based modulation to the carrier frequency. As the mix of chromosomes become too separated (cousins, 2nd cousins, etc.) the ability to demodulate the signal decreases. Get too far away (5th cousin?) and you can't understand what you're hearing at all—if it was near enough to your carrier frequency in the first place.
Everyone had a notch filter that excludes everyone outside the family. People can be born with too-wide a notch filter, allowing them to hear multiple conversations/families at once, driving them mad. They could also be born with too narrow a notch filter, causing them to become "deaf" to family members at a young age. The notch filter narrows as the individual ages, excluding one generation after another and one set of cousins after another until the individual becomes deaf.
And that's as close as I would recommend getting to real radio broadcasting in a biological context based on the premises of your question.
But, to seriously answer your question...
No, it's impossible for biological radio to ever exist. The selection of frequency, filtering, and the act of modulating are synthetic concepts that can't be replicated by biology in any way. Note that I am NOT saying telepathy cannot exist, which may use the electromagnetic spectrum. But that's something else entirely that has nothing at all to do with the human invention of R.A.D.I.O. ("Rural Area Delivery of Information and Organization," didn't know it was an acronym, did you?).
1 Yup, I just invented a new word. Think of it as a squishy-squashy mashup of Physiology and Economics. I define it as, "the price you pay to be who you are." I'm liking it the more I think about it. ©2022 JBH. Trademark pending. No touchy!
2 Like puberty, but don't use puberty. You need something that defines the moment of becoming a family that shifts the carrier frequency away from what the carrier frequency was for the progenitor's parents. I'll explain all that in the main body of the post, just know that you need some other event (call it a "second puberty") that precedes the ability to procreate and allows procreation that establishes this shift in the carrier frequency.
3 OK, ignore footnote #2. The minor shift from parent to child solves the problem and you no longer need a pre-procreation, post-puberty event. At least it does if you completely ignore trying to use specific frequencies! Remember when I told you to not actually try to use Real Life? If you try to work out how the child of parents A with frequency X marries a child of parents B with frequency Y who together create a grandchild with, what, frequency Z? This whole process fails really, really, really fast if you try to use specifics. Don't use specifics. Just define the world rules in terms of "Real Life Radio" and move on with your story.
4 You could have a LOT of fun with this. Over modulation has another name: noise. Static is nothing more than chaotic modulation on the carrier frequency. A family reunion could really stink because of all the static!
5 There are reasons other than that, too, but we're ignoring them. Simplifying... angels weeping... you get the picture.