View iCloud photos on iPhone
The app to use for viewing iCloud photos is the Photos app and not mobile Safari (or any other web viewer).

Tap on Photos and then go to the shared tab. All the photos you have access through over iCloud should be there.

If not, open the settings app and check the settings under iCloud -> Photos and that you're actually logged in with the same Apple ID as you are using to upload the photos. If you can't do that, be sure to invite the AppleID you use on the iPhone to see the shared photos from the uploading account. For most people, the account is one and the same, but you don't have to do it that way if you have reasons.