I'm deploying to Kuwait next summer but I have braces for my teeth. Is this a problem?

Braces are not a limiting factor for deployments.

I know that at Cp Arifjan they have a dental clinic so if you are based there you should be good to go; I believe that Cp Buehring also has one so as long as you are good to go at your SRP you should be straight.

Yeah, I would check and see if they have a dentist over there. Better to find out now and voice your concerns.