Should I continue in this environment?

It doesn't sound good for you, but your doctor would be the one to ask. I'm sort of doubting the asthma part of it re KFC, but of course I don't know. (I have asthma and not copd and am likely allergic to different things than you are.) But I can see the copd aspect of it, or regular ordinary irritation aspect of it. Indeed, it doesn't sound great for anyone, copd or not. Does the place have working hoods with fans?

Everything works but there is always some smoke that gets out into the kitchen, and the flour i work right over.

i would quit immediatly you have to consider the long and short term health problems you could face