TL;DR -- You've got to get clever to make it survivable
This is going to be difficult. I'm going to assume dragon talons are similar to scaled-up eagles', because (a) eagles are badass, and (b) I have stats for them. ;D
First, eagles grip hard:
A Bald Eagle’s grip is believed to
be about 10 times stronger than the grip of an adult human hand and can exert upwards of 400 psi
or pounds per square inch
Second, the pressure never lets up:
The talons are
closed by the muscles, anchored on the leg bones, by contracting the tendons. The tendons are
contained in tendon sheaths. Both the tendons and tendon sheaths have tiny ridges. When the
tendon is contracted the ridges on the tendons and the tendon sheaths interlock, creating a kind of
"ratchet" effect, enabling the eagle to maintain tremendous pressure on the talons without
continuously maintaining the tremendous contraction force on the muscle
So at least several minutes, being squeezed by sharp talons at 400 PSI ... that is not survivable. Not without geting tricky...
Could it be your hero is wearing plate mail? The armor would take the hit, and probably be severely dented, but might allow the guy to survive.
Another possibility is that the strike is flawed; instead of getting grabbed, the hero leaps at the last instant and grabs the dragon's leg above the talon. Dragon would realize that something is wrong, but figure hey, he's not falling off, and the chicks can get some good rending practice.
I'm not too worried about the drop at the end; assume that the dragon doesn't want to risk crushing its chicks, so the drop is pretty low. Also, the nest could have a nice soft lining of sticks, leaves, shed scales, dragon guano, and the remains of previous meals.
Update after comments: The question comes up of whether dragon might consider using a lighter grip to grab the hero. This could be made to work; depends a lot on just how "alive" the dragon wants the prey to be when dropping it off for the chicks, and how well it gauges its strike against the sturdiness of the prey. That is to say, a strike which would cripple a buffalo would obliterate a man. Also, we might have to avoid the whole 200mph power-dive...
So ... we can posit that dragon's chicks are getting bigger, they're ready for some "practice" prey. So dragon might have a mode where she very gingerly captures the prey with full intent of keeping it alive. This would not be done lightly, as she doesn't want to risk damage to herself, but is a good option for hero survivability.
Source of quotes: https://www.hawkquest.org/TA/XL/Gripping.pdf