If you mean "I'll show you !" in the sense of "I'll teach you a lesson", I think we'd rather say "Tu vas voir !", or "Tu verras" in simple future ("You'll see").
Yet we use "je vais te montrer" with quite a same conotation, but generally in a longer sentence, i.e. with an object to the verb "montrer". E.g.:
Laisse-moi le faire tranquillement (Let me do it quietly) !
Quoi ?! Je vais te montrer, "tranquillement" ! (What ?! I'll show you "quietly" !)
(in that example too, we could say Tu vas voir, "tranquillement" !)
It's not that set in stone.
It's rather that in everyday conversation, we commonly use "aller + verbe" for future tense, whether near or not. I can say "L'année prochaine / Dans deux ans, je vais faire le tour du monde / je vais changer de travail / etc." (Next year / In two years, I'm going to travel around the world / to change jobs / etc.)
On the other hand, simple future can also be used for near future : "Je lui parlerai tout à l'heure" (I'll talk to him later).
But theoretically, indeed, you use "aller + verbe" for relatively near future.
Well, as it is (and without a context), everyone would understand this sentence as "I will show you (how to do) something".
Grammatically, it can be "I will show you (to someone else)", but then chances are that "someone else" will be expressed in the sentence. I could imagine talking to somebody I have just put some special make-up on, or dressed with a costume, etc., then indeed I could say :
- Venez, je vais vous montrer à vos amis / aux autres / au public / etc.
You will find the answer here: https://www.thoughtco.com/french-object-pronouns-1368886 The object pronoun of the main verb is placed before the main verb.
If I wanted to change this to say "Will you show us?" Should it be Vous allez montrer? Vous vais montrer? Where does allez properly go in the sentence? And if I want to add an object, does it go before the infinitive: Vous allez nous l'montrer? or Vous allez l'montrer nous? Vous vais nous monster allez? Sorry if this is basic; I'm struggling with word order...
I think you mean the object is placed before the verb. The subject is "je". The verb is "vais". "Vous" is the indirect object of the infinitive "montrer". In English, direct and indirect objects are placed after that verb, but in French, they are placed immediately before the verb for which they are the object, i.e., montrer. https://www.thoughtco.com/french-object-pronouns-1368886