I suspect that if it still exists, it's in an unknown private collection. It is not in the state archives and there is no mention of it in the Texas State Historical Association records.
Organized spring/summer 1862 (mainly March–August). Served until the Trans-Mississippi surrender in May/June 1865 (included in the June 23, 1865 Doaksville surrender). Disbanded shortly after.
I agree that the odds of finding a relic are very small. Flags wore out & were regularly replaced. A large percentage of the CSA flags that survived were captured. At the surrender the 20th could have had a generic depot issue flag with no distinguishing marks.
I am sitting in front of a museum with many CSA flags. For most of them, the card next to the display is all that distinguishes it from any other. You have to take that with a large grain of salt.
What we can do is survey the flags of the TransMississippi. Unlike Virginia, there were a wide variety of battle flags. My personal favorite is VanDorne's.
CONTENTS OF THIS PAGE: The Missouri State Guard and other “Secession” Flags in Missouri State Flags and Company Flags in the Trans-Mississippi Confederacy The Confederate 1st National Flag in the Trans-Mississippi The Confederate 1st National Flag and Their Indian Allies The Second National Flag...
CONTENTS OF THIS PAGE: The Van Dorn Battle Flag The Battle Flags of Breckinridge’s Division /Army of West Tennessee. The White Cross Battle Flags of the Vicksburg Garrison First pattern Van Dorn battle flag of the 4th Missouri Infantry, 1862-1863 by Wayne J. Lovett from a sketch by Howard...
confederateflags.org
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These are reproductions of Texas cavalry flags. It is a taste of what the flag you seek could have looked like.