Hello garfyso,
Just to confirm, it seems like you want to download iCloud videos on your iPhone, is that correct? If so, the following link explains how to download photos and videos to your device from iCloud: Download iCloud photos and videos
On your iPhone, iPad, or iPod touch
1. On iCloud.com, tap Photos.
2. Tap Select, then tap a photo or video. To select multiple photos or videos, tap more than one. To select your entire library, tap Select All.
3. Tap the more button .
4. Choose Download, then tap Download to confirm.
If your photos download as a ZIP archive, learn how to uncompress the folder on your iPhone, iPad, or iPod touch.
To clarify, does the issue only happen with photos and videos? In other words, are you able to save other content to the Files app successfully? That information can help us get a better understanding of the issue.
You can also find some good information on using the Files app here: Use the Files app on your iPhone, iPad, or iPod touch
Thanks!