What is the dimension of the flat ceiling? Square or rectangular?

It is a rectangle about 15' by 22'

Depends on colors if the beams will be lost or not...that and sight lines. If you can't see ever the ceiling without craning your neck back, it may be money not well spent. On the other hand, if it can be seen, then using a contrasting color scheme will make it pop. Natural wood beams on white or light ceiling color... There may be a practical side to this as well. I posted recently about how to tame the acoustics in a great room...breaking up the hard flat surface of the ceiling helps that issue.

That ceiling is definitely large enough but waaaay up there. I'd give it a lot of thought before spending the money. If it were 8 to 12 feet, I feel its worth doing if that's a look that you enjoy