I THINK the black wire is the antenna in a Kindle Fire. It might be worthwhile just to run it out of the case and let it hang.
A little bit of an update on the kindle fire antenna mod I was wanting to do. I got the kindle all open and was ready to install an external Ipx or mini pci to rp-sma antenna pig tail extension wire. But when I pulled the plug off the kindles antenna wire to plug. The extension wire in is when I noticed the connector plug thats in the kindle is about 1/2 the size of a normal mini pci connector. They use whats called an "ultra miniature" pci connector. and i am having a heck of a time finding any place at all that sell either the pig tails with the ultra mini connectors on them and even having a hard time finding any female ultra mini connectors at all.
So far the only thing I came up with is to get some solder on rp-sma connectors and a cheap $5 kindle antenna i can chop off the wire with the ultra mini connecter on and solder it it to the rp-sma connector to make my own extension. It just sucks that I now have to wait again for parts to arrive and it ended up costing me $6 to make what should of been under $2 mod. Had it just had a regular mini pci connector in the kindle.