Perhaps it should be: "I'm not going to stand for that" which means I'm not going to tolerate something. You might say something like this in response to something you find unacceptable.

There should be a comma after "what" and then it makes sense. ("What, am I gonna stand for that?") To stand for something means to be able to tolerate it. The expression "I can't stand you!" means you can't tolerate this person. So, "What, I'm gonna stand for that?" means you're being defiant. You simply won't take this. You won't accept this.

The way it is written, it would not be correct. You would have to say it like this to make sense, and it would be you or someone else speaking: "What? Am I going to stand for that?" This means, you doubt that you will approve, or you doubt that you are agreeing with someone about something.

THe meaning of the statement as it is written would be closest to "How can I stand for that?" which is like saying: "How can I support that?" or "How can I except that?" Notice that these two meanings are opposite. This means you really must decide what you want to say, and find a new way to do it more clearly.

@ FWES, thumbs up mate. :)