I believe that Mexico still retains the Alamo battle flag. Perhaps you are thinking of another flag.
There are a number of historic artifacts that remain in Mexico. A painting of a siege in this region was given (back???) to Mexico a couple of years ago (it used to reside in the Houston MFA).
They might still have the flag. I remember back in the 70's when we were using Santa Anna's wooden leg for leverage to to get the flag back. I'm not sure where the leg is now.