Are you talking about logging into the Wyze app with your account? Reading your post, I get the impression that you’ve managed to get some version of the app installed on your device but that you’re having difficulty completing the login process. If that’s correct, then I wonder if you need to change a browser setting and/or try a different browser as discussed in this topic:
When you launch the Wyze app and tap the Get Started button, the Wyze app sends you to your device’s default browser to complete the authentication process, and at the end of that the browser is supposed to pass you back to the Wyze app, but that may not happen seamlessly depending on what browser and/or browser settings you’re using. I don’t know what browsers are available on Fire OS devices, but maybe something in that other topic will provide helpful ideas, and then you can share that if you find a solution.
The other thing I wonder about with login issues is VPNs. You didn’t mention using one, but VPNs have been known to cause a lot of users’ login problems, so you might consider temporarily disabling that if it’s an issue.