Will injecting Botox into the Buccinator muscle make my face appear slimmer?

Without pictures it is difficult to tell what is making your face chubby. I doubt that it is the buccinator muscle. There is a fat pad in that area called the buccal fat pad and that may be the cause of your chubby appearance. I would talk to a board-certified plastic surgeon about this and they may suggest excision of that buccal fat pad.Good luck! 

You have posted no pictures to indicate why your face is "really chubby". If its fat, then Botox will do nothing. If its Bone, then Botox will do nothing. If if excess facial volume is due to masseter muscle hypertrophy then longterm proper injection of Botox will atrophy the muscle and reduce the volume. Buccinator muscle hypertrophy is not the reason for "chubby" face and should not be injected with Botox as it will cause problems with oral competence.