@jbessette , Justin, That is strange that the shops you visited only worked on iPads, they must have had their hands full. Maybe go on line and see cell phone/computer repair shops listed and contact. Or if you would like to give the fix a try read below.
If port is found to be bad, this is really not a repair for the inexperienced usually, because the charge port for your Kindle is soldered to the mother board and the heat generated could cause further damage if not very careful. I will post a link to a tear down guide to get you inside the tablet to check the charge port and will also post a link showing what is involved in repairing a mini USB attached to the board. The last link is to new charge port, which you can also do a search for better pricing perhaps if needed.The whole Logic Board assy. can be had for $54.00 or less by searching if estimates to high by shops and then maybe worth you doing repair. If not wanting to do the repair yourself have a good computer/cell phone repair shop have a look and estimate repair. Good luck.
I hope this helped you out, if so let me know by pressing the helpful button.
Amazon Fire HD 10 Motherboard Replacement
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My charging port no longer works where is the best place e to send it that does not cost to much?