Can you defy Public Execution if it is played with Flow?

Yes — Defy can counter Public Execution even when it's played via Flow.

Defy checks the printed cost of the target spell (2 Energy, 1 Power for Public Execution), not what was actually paid. That printed cost is within Defy's range (≤4 energy, ≤1 power), so playing it from your trash for its Flow cost doesn't change anything — the alternate cost only affects what you pay, not Defy's legal targets. If the spell resolves, it still banishes itself as normal; if Defied, it just goes to the trash like any countered spell.