Can I fly with no ID?

 Your final remark about them not knowing how to read English does make me wonder whether this whole question is a big fat troll.

At Tijuana Airport you must pass Mexican immigration (they speak and read English) BEFORE you check in.

You will not be flying without one of the required Border crossing Documents.

THIS IS NOT AN AIRLINE problem.

Suggest you work on cancelling to rebook for a future date when you have the correct document. MOST use a Passport.

Did you report the loss of your ID and passport immediately you noticed? At a police station? And receive an official document confirming that you did report these losses?

If you did that, then it's just remotely possible that the airline might let you fly, if you show all your other papers. But don't leave it to chance: PHONE the airline right now, explain the situation, and ask their advice.

IF you give them advance notice that you won't have your passport and ID when you turn up at the airport, they MIGHT be a little more flexible than if you just waltz up saying "Hey sorry man, lost my papers, hope it doesn't matter".

Though I do have to add, your final remark about them not knowing how to read English does make me wonder whether this whole question is a big fat troll.

No ID = no option to fly

Okay. To get this straight you are traveling within Mexico domestically and you do not have a valid ID.

I'm going to have confidence that the checkpoints at Mexican airports is set up and run similar to that in the U.S. It is likely that the screening officers will be able to read English. It is also likely that they will only accept a passport for ID if you are citizen from a foreign country. 

My recommendation is that you bring your birth certificate and social security card with you. It will help. Get to the airport earlier than usual so as to give the screening officers ample time to confirm your identification and to perform what extra screening they deem necessary.

https://www.tsa.gov/travel/security-screening/iden... (See under "Forgot Your ID?". Again this is an approximation of what to expect. Mexico may have extra processes involved.)

@Ivan: Already experienced this which amounts to an immediate referral to the supervisor. (Passengers who behave like weenies don't get their way.. the checkpoint is not Burger King.)

What a stunningly ignorant remark! Are you in Tijuana or traveling there? While there may be ways to get into Mexico with the ID you have, you won't get back into the US without a passport. And the airlines have strict rules about identification for flying. You can get your passport from a consulate in one day. 

All immigration officials read English well enough to know what is acceptable ID and what isn't. 

It's not happening.  They are professionals who are trained to properly do their jobs.  Of course they speak and read English.

I don’t think it’s worth it. It’s always best to have all of your credentials in order. But, the worst that could possibly happen is they’ll turn you around at the gate

So you do have some ID. Give it a try.

I mean what have you got to lose

Call the airline but I suspect it’s a no

Just tell them that asking for ID is racist, and obtaining an ID is too big of a hurdle for you to get over.