Well, I have both a Kindle (a Paperwhite, not a Fire) and an iPad (9.7" 2016 iPad Pro).
Why do I have both, you may ask. Well...try reading an iPad outside in the sun. Doesn't work. And last year, Amazon had an amazing deal on the Paperwhites, so I got one, figuring it would be great to travel with, since it's small and keeps its charge for up to 6 weeks (!). It fits in my purse, so I can take it anywhere easily. And it is great - though I find I use the iPad when I'm at home - probably because I can do other things on it too. I do have the Kindle app on the iPad, and they sync, so I can switch from one to the other very easily. I belong to BookBub, so get a lot of very inexpensive and occasionally free books, as well as buying other Kindle books by favourite authors.
However - it should be noted that the Paperwhite is a different beast than a Fire. The Fire is more of a general all-purpose tablet. It has an LED screen, not the E-ink of the Paperwhite, so it has the same drawbacks as the iPad for readability in sunlight. Its screen is not as good as the iPad, nor is its camera; and you certainly don't have the Apple easy interoperability options (Mail, Messages etc.). Of course, the Fire is a lot cheaper, too.
I use my iPad a lot - for reading news, checking and responding to email, recording board meetings for which I'm secretary, texting, occasionally taking pictures, playing games (addicted to Hearts...LOL), and reading books - both in the Kindle app and the Apple Books app.
If I had to choose one or the other, I'd definitely go for the iPad because of its versatility/integration with the rest of my Apple devices, screen quality, camera quality, and just accept that it isn't useful outside for reading (though neither is a Fire). You can get pretty good deals on the refurbished 6th generation models on the Apple refurb store at the moment. Still more expensive than a Fire, of course.
If you decide to tackle putting in a new battery, this site might be a good source:
https://www.newpower99.com/Amazon_Kindle_Fire_Battery_Replacement_Kit_p/amazon%20kindle%20fire.htm (I'll leave you to find the right one though). Looks pretty easy...