Is wearing a flag patch on a backpack against regulations?

While there is nothing specific in 670-1 regarding placement of a flag on a backpack, your CSM is well within their rights to say no. This is one argument not worth fighting.

Are you talking military or civilian??? I don't believe there is a civilian regulation about wearing an American flag on a backpack!!! That's just patriotic!!! As far as military goes, I never saw any kind of patches on any backpack I ever wore while in service!!!

I may be wrong but I will say yes.

no it's not

In uniform, be in uniform! Out of uniform, be "respectful".

yes

I do not know.

Seems like a bunch of people are assuming your CSM called you out, though this may not be the case.

For clarification:
If your CSM called you out, stop being a dirtbag.
If not, the person has no idea what they are talking about because no it isn't. It's a patch and not offensive. Unless the backpack is part of your uniform, then any unregulated patches are against regulations.
I once had a bored LCDR go off about those of us with camel backs that were black because his wasn't and we apparently should have all matched him. Even though our black ones had been previously issued and his was bought at the Exchange. That guy was a prick though, I'm surprised he didn't make us all wear BCGs like him. Like was mentioned by others though, pick your battles.

Yes

I don't care what fashion desisigner "reimagined" Army uniforms, the field should be on the left!