I would just air it outside for a long time. I like the idea of turning it inside out also. It may take days to get rid of all of the smell.
Another option is to place the jacket in a plastic bag along with a couple of pairs of Odoreaters brand shoe inserts (the ones with charcoal) and seal the bag for a couple of weeks. Charcoal absorbs odor. Check on Amazon for other charcoal options. I like the shoe inserts because there is no chance of the charcoal spilling and they can be used in shoes afterwards! (I used these insoles to get rid of the musty smell in a featherweight case.)