The flow is a little bit different between the two examples (Roku requires you to enter your username and password, while the Fire app utilizes a Device Code system) but they both connect to the same database of users to verify your credentials.
Roku login trouble
The Roku devices will typically try to automatically put your Roku account's email address into the E-mail address field. However your account on the website may or may not use the same address since they can be different. Things to try instead:
1. Verify that the email address you're signing into the app with is correct and free of typos;
2. Try logging in using your username instead
3. Update your password by sending yourself a Password Reset Link.
FireTV Login trouble
Since the FireTV app requires you to sign into the RiffTrax.com website on a browser (or mobile device browser), any login issues may be the result of your account not existing, being disabled, or using a different email address. Things to try:
1. Make sure your browser isn't overriding a typed password with a saved one! Sometimes Google Chrome in particular will overwrite the username/password fields with a previously saved value that could be outdated.
2. Try logging in with a different email address, or your username.
3. Did you use Facebook to register for an account? If so, you may need to reset your password by sending yourself a Password Reset Link.