Enamel paints polymerize into a sort of plastic film that is very flexible. They also bond very tightly to most surfaces. Lacquer paints tend to be much more brittle. Water-based Acrylic paints are usually nice and flexible, but they aren't as good at adhering to surfaces.
One thought to your armpit problem would be to try applying a couple different types of lubricant to the surface after painting. I haven't tried this, so I can't say which would work best. Possibly a silicone oil such as found in certain specific...ahem..."personal" lubricants. It would cause that area to be glossier, but it would reduce friction, which is what causes the flaking. Keeping the area constantly powdered would have a similar effect. This is why gymnasts and pool-players alike "chalk" their hands (it's more often talcum powder these days). You could potentially produce a tinted powder by mixing a tiny amount of pure cosmetic pigment and mixing it up, and this might reduce the chalky appearance it would produce on the surface (assuming you aren't already painted white). I've never tried this though.