flick is a rapid motion, often with a snap or other short noise, often using your finger or thumb.

Like "he fished a lighter out of the pocket, flicked it open and ..."

Flick a switchblade is "открыть нож" in my opinion. Also it's "выщёлкивать" -- он выщелкнул лезвие выкидухи...
Sometimes "щёлкнуть" is already sufficient.
Like "он щёлкнул выкидухой", in an appropriate context it feels right and doesn't need additional elucidation.