Would it be right to write "Brazilian's army's ammo supply is low."? Two consecutive apostrophes looks weird.
It would depend on what you meant. If you mean the Brazilian army was short of ammunition, then you would write the Brazilian Army's ammo supply is low.
But if you were referring to an army that is not the Brazilian army, but instead owned or run by a particular Brazilian (perhaps an army of toy soldiers, or an army of mercenaries), then the Brazilian's Army's ammo supply would be correct.
To be honest there are cases when it's perfectly acceptable to have "dual 's"
For Example: "Bob's army's Supply was lower then normal after the storm."
That said, it's probably best to avoid it. Specially when listing a "general" term.
For Example: "The Brazilian's army's Supply was lower then normal after the storm."
Both cases are "correct" but they both read very odd. It would be better to rewrite the sentences so that you could avoid the oddness.
Example: "Bob's army found its supplies lowered after the storm."
Example: "The Brazilian's army found its supplies lowered after the storm."
Those read much better, and removes the ambiguity in your original sentence.
Example: Brazilian's army's ammo supply is low.
Becomes: The ammo supply of the Brazilian's army was low.