too bad it was not the reverse...the wet suit would have been easier to handle.
The first approach is to take all the items that are washable (fins, mask) and do the washing. Then let it air out in the sun...if possible. If not, air it out in a dry, warm room.
For your reg, wash off the exterior parts with a mild detergent/water solution. The metallic parts cannot mildew or absorb mildew, but there can be mildew adhering to the surface of the metal. It should come off readily. If the smell does not come off the rubber parts, you can have them replaced...and it will be costly. So, give a real good try.
The BC is another problem. If the mildew got into the bladder, you have to clean that out. We usually clean the inside of the bladder by unscrewing the fitting that is used to attach the inflator hose to the BC. Then you can rinse with fresh water. You can use a mild detergent there, too; just be sure to rinse carefully.
Something we have never done, but you might consider is to use one of the mildew removers that you find in supermarkets. Read the label carefully to make certain that they do not harm rubber, plastic, etc. I would try it on the fins first... But, again, I have never used that material.
Finally, the take home lesson is to wash and rinse your gear when you get home and hang it up to air immediately.
Joewr