You're on the right track in identifying that the Potassium ion is the most common ion that flame-tests something that might be described as purple; and Potassium is abundant in sea water, and biologically compatible. The question, then, is what biochemical pathways lead to high concentrations (1000+ ppm, I'd imagine, is needed) of Ka+ in fat deposits.
Really, you can choose any non-soluble Potassium salt, posit a reason for it to form in your creature, and then safely assume (a) a transport mechanism to move the precipitate or preferentially precipitate the salt in fatty tissues (since the absence of such a mechanism would put the creature at risk of e.g. kidney stones and other obstructive diseases, this would be evolutionarily favored) and (b) a mechanism to extract sufficient potassium (in the form of potassium chloride) from seawater (which already exists, but would have to be more active due to the loss of potassium from precipitation in this case).
One challenge is that very few potassium salts are particularly insoluble, so you're going to have a hard time getting the concentrations high enough (without other biological consequences) for precipitation. Ideally you want to precipitation to occur at blood / body fluid concentrations low enough to not really effect osmotic pressure or anything. Still, options exist, including just running a somewhat-insoluble salt at super-high concentrations -- perhaps as a biological antifreeze -- and solving the osmotic pressure issue another way.
If you want something more fun, and that may guide plot, one salt that comes to mind is Potassium hexachloroplatinate. Suppose a whale-type creature that is able to go to deep depths, beyond what is accessible to your humans. Suppose also that something -- most likely an ancient meteorite -- has deposited a huge mass of relatively pure platinum on the sea bottom in the midst of this creature's habitat. Suppose that the creature is ingesting so much platinum that its actually at risk for metal poisoning -- for example, it's a filter feeder evolutionarily, a delicious type of brine shrimp has decided that the rubble of this meteor is its home, and your filter feeder has started to get excellent meals by scooping piles of platinum-rich rubble into its mouth and filtering out the good stuff -- but also an uncomfortable amount of platinum. (The major problem with this is that metallic platinum is really, really not bio-reactive, so the amount needed to be poisonous is absurd -- but hey, due to evolutionary chance your creature is sensitive to it.)
A technique of removing platinum is needed, and given the abundance of biologically available chlorine, coordinating that platinum into PtCl6(2-) is a perfectly reasonable pathway to take. This will form Sodium hexachloroplatinate in the (sodium ion rich) blood stream, which is soluble and fine; but the creature needs to not just coordinate the platinum but also eliminate it from the blood stream to avoid accumulative poisoning. Fortunately, it's trivial (evolutionarily speaking) to transfer selective ions across cell walls; and the fat cells specifically evolve to do so. When the Sodium hexachloroplatinate enters the potassium-rich cytoplasm of a cell, some Potassium hexachloroplatinate will form, precipitate out, and the reaction will continue until the platinum is eliminated, or reduced to a low level, in the blood stream
In this way, over time members of this species that filter-feed on the platinum-rich detritus of the meteorite will concentrate Potassium hexachloroplatinate in their fat tissues. When purified and burned, this oil will burn a violet/purple. Like most oils, this will burn with very little ash (solid residue)... but what ash there is will be very rich in platinum that can then be purified. So the purple oil is valuable not only for its beauty, but because it gives a source of a rare and valuable metal.
And of course if one were to try to raise these creatures in captivity, their oil would not burn purple, and there would be no platinum to be found...