It's a person who is like a lifestyle coach , who helps actors look and behave in a certain style. For example Justin Bieber has one. He helps him develop his natural talents. A lot of professional American athletes also have swag coaches.

It means the way a person present himself/herself: looks, style, confidence, etc. example: did you see that girl? she's got swag. So probably, a swag coach is a person who'll be teaching you how to have that swag--the looks, style and appeal that will make you look cool.