How much paint are we talking? If it were mine, for piece of mind, i'd take it out the road and treat it like new pads. A couple of good hard stops to make sure it doesn't catch you off guard when you are plowing toward the back of another car.
Having said that I really doubt it'll do anything - just piece of mind.
lol.. Brake calliper paint is heat resistant so it won't flake under the high temps. You might find that your paint won't last to long if you used the wrong one. I'd give it a month and it'll look rubbish and need a respray.
You might be able to just sand what you have back a bit with some wet and dry and then just paint over with the proper stuff. You can also use engine enamel as it's a heat resistant paint too.
First half hour of braking they might stick so try not to stop. (heat makes it sticky)
As mentioned.. treat them like your bedding in new pads. Try to brake as hard as you can the first time you take it out.
And yes youll need proper brake paint. Normal paint will burn, fade and peel under the extreme heat.