To my knowledge there are no tested and approved instructions for making vinegar from figs simply because figs, unlike most other fruits, are a low-acid fruit. So pH safety is going to be an issue one wouldn't have when making vinegar otherwise and that pH may well allow for the development of pathogenic bacteria and molds unless some additional acid is added to the mix. How much? No way to know for sure. For that reason alone I wouldn't do it.

But there are web recipes for making it at your own risk and most call for the addition of red wine vinegar to the fig puree.

Example: (not recommending it, just offering it as an example)

http://www.cooksinfo.com/fig-vinegar

If you decide to do it please keep in mind that for safe consumption and storage it will need to be pasteurized once made.

Dave