I have the setup you describe....SWCG and natural flagstone, and am also in Central Texas. It was sealed by builder upon completion 2 years ago. I have not seen any evidence of the flagstone being eaten away. I plan to seal the flagstone again shortly and contacted my builder for the recommended product. Got the recommendation and a local supplier.
I also have huge pieces of flagstone down in the back yard as stepping stones leading to the pool and smaller ones to the pad area and all around the pad. They all get copious amount of salt water on them. Not to mention the sprinkler system which is way worse than the pool. Again, no known issues. I regularly inspect for any cracks, crevices, chips, flakes, etc.
Now I do not know if mine is Oklahoma flagstone or not. I've never heard that modifier on it....but I never heard of different types of flagstones when we were discussing coping choices with my builder.