iPhones don't have a right-click "Save video as…", and the RedGIFs app has no save button. The reliable way is a browser download, then one tap to move the clip into Photos.
Step by step
In the RedGIFs app or Reddit, tap Share → Copy link on the video.
Open redgifs-downloader.com in Safari and tap the clipboard button next to the box (or long-press the box → Paste).
Tap Get video, then Download HD (or Download SD for a smaller file).
Safari asks whether to download — tap Download. The download arrow in the address bar shows progress.
Open the Files app → Downloads, tap the clip, then Share → Save Video. It's now in Photos.
If the video opens instead of saving
Depending on the iOS version, Safari sometimes shows the clip in a player tab rather than downloading it. That's fine: tap the Share button and choose Save Video, or press and hold on the video and pick Save Video / Download Linked File.
Tips
Sound: the result card says "with sound" or "no sound" before you download. If a clip plays silently in Photos, check that first — some clips were uploaded without audio (why).
Many clips: paste several links at once (one per line), then use Download all; Safari asks once per file.
Images and galleries: they save as JPGs; open them in Files and Share → Save Image. See images and galleries.
Add to Home Screen (Share → Add to Home Screen) to open the tool like an app.
Safari saves them to the Files app, in the Downloads folder (iCloud Drive or On My iPhone, depending on your Safari settings). Open the file and use Share → Save Video to put it in Photos.
Why does the video open instead of downloading on my iPhone?
Some iOS versions and browsers open media in a player instead of saving it. With the video open, tap Share → Save Video (or long-press the video and choose Save Video).
Does it work in Chrome for iPhone?
Yes. Chrome on iOS uses the same engine as Safari; downloads end up in the Files app the same way.