if jayce man of progress kills a gold gear token do you get the added power from the gold. if so can i use that power to pay for the vanguard armory that ill also use from his ability

No, and it matters why — a Gold token killed by Jayce's trigger adds no Power. Jayce's "you may kill a friendly gear" is an "if you do" instruction that happens during his trigger's resolution, not a cost, so it never activates the Gold token's ability. The 1 Power comes only from activating the token's own ability — Kill this, [T]: [Reaction] — Add [A] — where killing and exhausting the token are the costs. A Gold killed by an outside effect just goes to the trash (same one-Gold-one-use logic as the Malzahar ruling).

Yes, that Power can pay for Vanguard Armory — but you need two gear. Kill a different friendly gear for Jayce's trigger, then activate the Gold token's own ability (it has Reaction + Add, so it finalizes and resolves immediately, Rule 429.2). The resulting any-domain [A] Power covers Vanguard Armory's 1 Order Power, since Jayce only ignores its 7 Energy cost, not its Power cost.

Sequencing note: if the Gold is your only gear, activating it for Power means Jayce's "if you do" can never be satisfied, and you get no gear play at all. And per the Jayce clarification, the free-ish gear play happens any time after the trigger resolves, still that turn — so rune pool Power you're holding stays usable.