If my opponent uses a Wages of Pain on my 4 might unit at a Forbidding Waste battlefield and then moves a unit onto the battlefield, do I have an opportunity to use flash before my unit dies?

Yes — you have a window to use Flash before your unit dies.

Here's the timing breakdown:

1. Wages of Pain goes on the Chain → State becomes Closed. You get priority to play Reaction spells/abilities.
2. Flash is a [Reaction], so you can play it right now. It goes on the Chain above Wages.
3. Flash resolves first (LIFO) — you move your unit to Base. It's now safe.
4. Wages then tries to resolve, but your unit is no longer at the battlefield. The damage instruction can't be executed (illegal target), so it's ignored. (The Gold token is still made as a separate instruction — FAQ #9528.)
5. If you don't Flash during that window, Wages deals 3 damage. Your 4-Might unit at Forbidding Waste alone has effective Might 2 (from the -2 penalty), so 3 damage = lethal. It dies in the ensuing Cleanup before your opponent can move a unit in (FAQ #11041).

So the only window to save your unit is while Wages of Pain is on the Chain. Once it resolves and Cleanup starts, there's no further opportunity to react.