We haven't been to T-Rex and tried to eat GF, but we have eaten GF at our local Rain Forest Cafe (we live in Houston). Both restaurants are owned by the Landry's company. The Rain Forest Cafe did a great job with my DS's food allergies. We called ahead, and they were expecting us. The chef came out and talked to us about what would be safe, etc. DS ended up with a cheese burger (no bun) and fries, I think (it was over a year ago!),-- DS's tolerance to wheat is high enough that he can have cross contaminated fries (cooked in the same fryer oil as wheat products) and still not have a reaction, so I can't remember if the fries were cross contaminated or not. Anyhow, Rain Forest Cafe was very accomadating, so I imagine that T-Rex would be the same.
The Disney owned restaurants seem to go totally above and beyond, though, and they actually carry things like GF dinner rolls, hotdog buns, tinkyade rice pasta, etc. I don't think that the T-Rex cafe would carry specialty GF items (although I don't know for sure) like the Disney owned restaurants do. Anyhow, I hope my info helped a little. Maybe someone who's actually eaten there can chime in! --Katie