Does a counterspell that counters a spell with flash work if cast in response before it resolves?

Flash (CR 702.8) grants permission to cast a spell at times you normally couldn't — specifically, any time you could cast an instant. It does nothing else. Once a flash spell has been legally cast and placed on the stack, it is treated like any other spell awaiting resolution.

When a spell is on the stack, any player with priority may cast spells or activate abilities in response (CR 116.2). If an opponent casts a flash spell during your turn, you receive priority after it is placed on the stack and may immediately cast a counterspell targeting it (CR 116.3).

Counterspells simply require a legal target — a spell on the stack (CR 114.1). A flash spell on the stack is a perfectly legal target. Flash provides no protection against being countered; for that, a spell would need an ability like 'This spell can't be countered' (CR 701.5a).

Concrete example: Your opponent casts Vedalken Orrery and then, during your end step, flashes in Mystical Snake (a creature with flash and a counter-target-spell ability). You still have priority after it's put on the stack and you respond by casting Cancel targeting it — Cancel resolves first and counters Mystical Snake before it ever resolves.

In short, flash changes casting timing only; it grants no immunity to countermagic once the spell is on the stack.