I certainly do not expect anyone to change anything based upon my humble opinion, but I do not believe it appropriate to have the flag of a nation permanently displayed in a church.
On some occasions, I can see it being used (such as draped over a casket during a funeral or in a procession of veterans or boyscouts, etc.), but it should not be standing or hanging or otherwise on display on a regular basis.
To me, the church is above and beyond nationality. At least it should be.