Hey Melindaea3,
We'd be happy to help out if you're having issues playing videos without interruption.
To get started, do you happen to be using iCloud Photos? For help with checking, go to Settings > Photos. For more info, check out: Set up and use iCloud Photos - Apple Support
If you are using iCloud Photos any photos and videos you've saved and are storing on the phone may also be stored on iCloud if Optimize iPhone Storage is enabled. If there's then a connection issue, this could be impacting your ability to play your videos smoothly.
Next, we'd suggest testing on cellular if on Wi-Fi, and on Wi-Fi if on cellular in order to isolate things further. If the issue only happens over Wi-Fi, restart your modem and router and test further. If happening on cellular only, move to an area where there's a better connection and test further to see if it's still behaving this way.
We hope this helps out. Keep us posted on how things go and what you find out.
Take care!