When our own Kindle Fire connectors started failing one after another we did the most natural thing for an electronic service center - opened all of them up, started messing around, hacked a few rough working solutions, bricked or two and eventually read manuals and watched videos of others doing the same.
At the end of the day we ended up purchasing a bunch of micro USB connectors like the one shown on the picture.
It is NOT the original connector used in the Kindle Fire, but we've used it with success and now that it's been more than 3-4 months of use with it we feel confident it can also be used by others.
There are a few major points you need to known when considering to use this connector:
1) It is the same height as the original so it will appear in the appropriate place in the opening
2) It has two small plastic legs at the bottom meant to go in holes in the board; the Fire does not have openings there and we simply cut the legs - any effort with pliers or even finger nails will be sufficient to cut them off and level the surface
3) There are two solder joints on each side, but they do NOT match the ones on the Kindle; you can use the front pair and bend the back one to avoid problems , but in that case you will run into a little too short connector pins or you can use the back pair and bend the front one (to stay out of the way) in which case the pins will solder nicely on the pads, but the connector will be 1 to 2 mm behind the wall and that can cause issue with some of the charging connectors just not reaching in enough. Most of them do work, however.
4) Since only two points of the connector can be originally soldered we manually solder the other two directly to the metal corpus of the connector. It is delicate, but completely doable procedure and the most you need to watch for is solder NOT going up and inside the body of the connector as it will present problems later when you plug in a cable.
That is pretty much it...we've done over 10 devices now and while the first one took 2 attempts and 2 hours the last one was in and out in 20 minutes.
It isn't a perfect substitute, but that's what you get for the money :-)
We would also gladly do the service for you if you ship your device to us...$40 plus return shipping is just prohibitive price though.
We can also give discount for a higher volume (multiples of 10).