“会” is required here because the sentence contains the meaning that "brush teeth after dinner" is a habit for him and that he will do it everyday. Adding "会" makes the sentence sound more naturally, in other words, makes more sense.
Is there anything wrong with saying
”吃完饭以后,他马上会刷牙” ?
The English says “after finishing meals”. Surely with just “吃完饭” on its own it only means “finishing meals” so ”以后” is needed to convey “after finishing meals”?
"会" implies that this is a statement about future events and not a discussion of a past/present habit. As such, there should be a corresponding "will" or even a "will always" in the English