Use purchased music only
For music from iTunes, ensure the track is bought (not from Apple Music catalog). Purchased tracks have a download icon and can be used in videos.
Import via Files app
If you have audio files on your computer, you can transfer them to your iPhone/iPad via iCloud Drive, Dropbox, or USB, then import them from the Files app.
Use royalty-free music
Consider using royalty-free music from services that provide downloadable MP3 files without copyright restrictions.