Any time the coin is on the table:
-- gravity acting downwards
-- normal force of the table, acting upwards
Any time the coin is moving:
-- friction force, on the coin's underside
-- air resistance
Both of these act opposite to the direction of the coin's motion.
During the flick, while your finger is still touching the coin:
-- the flicking force, a push exerted by your finger
The force ends as soon as the coin leaves contact with your finger.