Incorporating capsicum oil into a chicken breading
Breading chicken usually involves three stages:


Dip the chicken in flour to provide a uniform surface for egg to stick to
Dip it in an egg mixture
Dip it into bread crumbs or some other coarse, dry coating that will be the final texture.


Obviously the oil would not work in stages 1 or 3 because it could not be well distributed and would clump.

It is easy enough to add wet flavoring agents to the egg mixture. You should beat it well enough to partially emulsify the oil into the eggs so it doesn't all separate out on the first piece.

As Joe commented above, this seems like more trouble than it's worth. Mixing any kind of dried, ground or crushed peppers into the 3rd stage is much simpler. I use dried, crushed chipotles for this purpose.