You flip the coin when the ability resolves (C.R. 608.2c). While the ability is resolving, no player has priority (C.R. 116.2e), so, for example, you can't cast any spells between the coin flip and the destruction of permanents (if any) (review C.R. 116.1a). Rather, you can "respond to" that ability only before it resolves (so before you flip the coin) (C.R. 116.7), and after you activate that ability.
can i respond once i know the outcome of the coin flip or only to the activation?
thank you
EDIT (Mar. 18, 2019): Correctness edit.
EDIT (May 29, 2019): Add rule citation.