Yes, the gift Camerupt and Sharpedo from the Battle Resort apparently can be shiny.
Doing some research online, a lot of the gift Pokemon (except like Cosplay Pikachu) can be shiny, since Game Freak wasn't throwing out too many shiny locks yet, and the gift Camerupt and Sharpedo at the Battle Resort are examples of shiny gift Pokemon. I've seen other people talking about getting one shiny but not the other, so you aren't alone.
As for the chance to get these shiny, they each have a 1/4096 chance (standard shiny odds in this game), so consider yourself lucky!
