I left TX two years ago (Austin area). Heat indexes triple digit, like 60 days in a row, and then a freak storm that dropped half a bucket's worth of rainfall in just an hour or two, washed out two of our bridges.
If I had to do a coop there, I'd do a 3 sided "shed" design, single-sloped roof, big overhangs with the back wall oriented into the prevailing winter wind, under eave ventilation, and the front side open to a large fenced run, at least partially covered. That gives you your weather protection when you need it, keeps cold drafts of the birds in what passes for winter, and gives them lots of shade and airflow the rest of the time.
Minimally frame it, and forget the decking and shingles. Metal roof. Faster. Cheaper. and will reflect much of the brutal TX sun, rather than absorb and radiate it, as a shingle does. Also, fewer penetrations, less likely to leak in the long term.
With some modifications, I'd be building the right half of the building shown
- here - and extending the caged run where the left half of the building is presently. Would target a 4x8 footprint for the walls. Plenty of room for nest boxes, roosting bars, food and water if needed in bad weather, with a human door on the side for your access.