Upvote:4
Flights.google.com shows that flights between Reynosa, Mexico and San Jose del Cabo, Mexico, all connect via Mexico City.
This MEX Airport FAQ webpage contains the following text:
Documents for traveling on a domestic flight:
Mexicans
Boarding pass and an official identification (voter ID, passport, driver's license)
Foreigners
Boarding pass and valid passport
Thus, if you are a Mexican citizen and have a valid Mexican voter ID, Mexican passport, or Mexican driver's license, you can take these flights.
The documents you list in the question (birth certificate and Texas drivers license) do not meet the requirements set forth on the FAQ page.