Use Safari, not Chrome
On iPhone, Safari provides the best download experience. Chrome on iOS may not trigger the native download dialog. Open ClipKeep in Safari and tap the download button.
Save to Files app
When Safari presents a download prompt, choose Save to Files. The video will appear in the Files app under Downloads and can then be imported into Photos.
Storage space
Ensure your iPhone has enough free storage before downloading. A typical HD video can be 50–200 MB. Check Settings > General > iPhone Storage.