I am not sure how you are watching TV on you Fire tablet, Vic, as I do not have a Kindle. However, I do have a tablet and for that I need to register individually with BBC iPlayer, ITV Hub, All 4 and My5 TV and then I get about 20 of the most popular channels, live, as well as some catch-up services - all free. All you need to do is go online and visit each service - just Google.
An alternative for many more channels is the TV Player app for Kindle but it is a subscription service at £6,99 per month.
There is also an aggregator at
https://www.filmon.com/tvguide/ to view UK TV in your browser when online. UK only but works from anywhere so long as you have an Internet connection. It's not quite as stable as the ones mentioned above but it does the job.
And just to be clear. None of these need a TV dongle, viewer software and an aerial connection, they are all online.
Good luck.