Indeed - and this flag is held by the Chicago Historical Society today.
What Gracie's Brigade carried prior to going east into the ANV is somewhat problematic. There's two flags of Hilliard's Legion that survive, one the Army of Kentucky pattern (predates that pattern actually) and the other an ANV style rectangular (and small) flag that was shot up at Chickamauga. I will have to check their order of battle to see what else might be out there.
Greg Biggs