Spoiler 
The combination: bark + stick =makefire and has to be performed while looking at an unlit campfire. Once you have fire, take a branch in hand and use [e] it in the fireplace to make a torch. The torch in hand, although not alight in rain, will reignite when the rain stops, so you can take it in hand and whack a fire place a few times to get your fire burning again.
or instead of using the combination over a fireplace, find 2 "flint" on the first island, then attack the fireplace with 2 flints