Can I legally carry my gun in a flight from Texas to Mexico City?

It is a Federal crime in the passenger compartment, and in luggage need to check the airline rules, because carrying it through TSA security is not allowed.

Then, you have to deal with the Mexican entry.

I believe you need their permission. 

If you do not declare it, it is smuggling a weapon in, and they will be extra harsh. If you declare it, they probably confiscate it. You will have to check the importation laws yourself for firearms. Private citizens cannot carry firearms without permission from the government.

Not a chance. You can't board a plane with a firearm, and you have no 2nd amendment rights when you leave the USA.

nothing is holding you back