If my opponent plays Promising future and from that effect I play Zaun Punk can I wait to see if my opponent plays dazzling aurora to use my zaun punks effect?

Yes. Zaun Punk's "kill a gear" target is chosen at finalization of its "when you play me" trigger, which happens after Dazzling Aurora has already entered play — so you can wait and kill it.

Here's the timing: During Promising Future's resolution, your Zaun Punk goes on the chain first (you're the next player), then the opponent's Dazzling Aurora. Pending items finalize in the order they were added (Rule 337.1.b). Zaun Punk finalizes first and enters play, putting its "when you play me" trigger on the chain as a new pending item. Dazzling Aurora then finalizes and enters play. Only after that does your trigger finalize, at which point you choose the gear to kill (Rule 402.2) — and Dazzling Aurora is a legal target.

One catch: the decision to pay the additional cost (kill a friendly gear) must be made when you play Zaun Punk, before you know what the opponent picks. If you pay it up front, you get to choose Dazzling Aurora as the target afterward; if you don't pay it, the trigger never happens.