You're right that "I'm going to go" is entirely correct in any dialect of English. I never care about formal language. If a native speaker says that 'this is correct' I consider it correct as well. When my university teacher (who I don't quite like) says that what I say is not grammatical I just keep silent and think: How does she know what is grammatical and what is not? Then if I tell her that a native speaker read my essay (for example) and said that it's fine that means it's fine. I have never learned formal language. I study English to communcate with other people. To me, it's strange to see formal posts when discussing commonplace things.btw I think "I'm going to go..." is 100% formal and correct by any standard in any variety of English; without "to go" it's probably colloquial but still fine to use, imo.