1-hit kill: one hit of that particular weapon or attack type (kick, throw, smash, normal, etc.) and the mob/boss is dead.
1-Flinch: Just needs one hit to break off the part (usually made with sticky bombs).
Sticky Kill: I believe you mean Sticky Bomb, they are used to break off parts of break-off-able bosses and they don't need to be accurate (eg: spears). You throw the bomb at the boss or anywhere in the room and BOOM, there goes your break off.