In my humble opinion:
The flag piece does not blend with the other fabrics - as a backing it would be OK
I would not fussy cut. You have 4 beautiful coordinating fabrics, why chop one up?
Not knowing how much you have of each: how about a log cabin or mixed nine patches or even a disappearing nine patch?
If you cruise the web you'll find lots of great patterns for 4 fabric quilts.
BUT - this is just my opinion...............