I play Promising Future, I play Elder Dragon from Promising Future, opp plays Harness Dragon from Promising Future, what is the result?

Both dragons die — it's a trade.

Promising Future plays cards "starting with the next player," so in 1v1 your opponent's Harnessed Dragon is finalized first, then your Elder Dragon. Both "When you play me" triggers go on the chain in that order, so Elder Dragon's trigger resolves first (LIFO): it deals 1 to Harnessed Dragon at its location, and because Elder Dragon's passive makes any of your damage lethal, Harnessed Dragon is killed. Its trigger was already on the chain though, so it still resolves and kills your Elder Dragon — a kill isn't damage, and Elder Dragon's passive doesn't stop it.

One caveat: if Elder Dragon were somehow played first, the result flips. Harnessed Dragon's trigger would resolve first, killing Elder Dragon before its own trigger resolves. With Elder Dragon dead, its passive is inactive (Rule 365.1), so its trigger would deal only 1 non-lethal damage to the 6-Might Harnessed Dragon, which would survive. Per the rules, though, the opponent plays first via Promising Future. Note both triggers resolve on a real chain afterward, so Reactions (e.g., Not So Fast) can be played then.