I can certainly scan it and send it to you. But I want you to keep in mind a couple of things.
The image that exists is rough -- basically colored pencil at the foot of a handwritten memoir. It's not big, not detailed and kind of abbreviated, as it is at the bottom of a page.
Too, the image exists because the flag (and two U.S. artillery pieces) were captured by Santa Anna's troops. (The cannons were recaptured outside Mexico City and their wheels are in the admin building at West Point.) This was not exactly a proud moment for the men in the First Arkansas Mounted Gunmen who lost that flag (or flags). They were accused of fleeing the battlefield.
But if you want it, I'll try to get it to you in 24 hours. It's the least I can do for Arkansas servicemen in another foreign war.
I'll need an e-mail address, I suppose.