If your YouTube app is freezing on your Amazon Fire TV stick try the following:
1) Go to Home on Fire TV > then in the top menu, select Settings > Applications > Manage Installed Applications > Firefox > select to Clear Cache.
(Note: if you're using the Silk Browser, you should Clear Cache for it as well).
2) Now do the same for the YouTube app in Settings > Applications > Manage Installed Applications > YouTube > select to Clear Cache.
3) Now go to Home > then reopen the YouTube app. Hopefully, YouTube will be working correctly now without freezing up.
Note you can clear the Cache for all your apps, to free up space on your Firestick device.
If you continue to experience problems, you can Clear Data from the Firefox and YouTube apps and Force Stop. But keep in mind, clearing data will cause the Apps to lose all bookmarks, settings and passwords that you’ve set up.
1) Go to Home on Fire TV > then in the top menu, select Settings > Applications > Manage Installed Applications > Firefox > select to Clear Data. Then do the same for YouTube.
Lastly, I recommend you turn OFF your internet Cable Router and WiFi Router, and then restart. Then restart your TV / Fire stick. Sometimes, the internet connection can cause a slow down of Fire TV.