Its better not to let your child watch tv while eating.
My boy is 3yrs + but he eats at the pace of a snail... We did encourage him to self feed. He does, but he likes to talk with his mouth full, play around or just day dream.
Sometimes we have to feed him instead to get him to finish his food faster.
His teacher complaint that he doesn't want to eat by himself at school and wants the teacher to feed him.
And he can never finish his food while watching tv, he can take more than 1 hour to finish, he will place the food in his mouth, chew for a while and stop. So its better not to make it a habit to let them watch tv while eating.