how do I get the photo app added to my icloud?

There are no apps for Google Chrome OS.

You’ll have to use the iCloud website to view your photos from a Chromebook, or use the iPhone or another Apple device.

Here is how to set up and use iCloud Photos: https://support.apple.com/en-us/HT204264

Have you turned on iCloud Photos on your phone and allowed time for the photos to sync to iCloud? See the following from Set up and use iCloud Photos - Apple Support

On your iPhone, iPad, or iPod touch

1. Go to Settings > [your name].
2. Tap iCloud.
3. Tap Photos, then turn on iCloud Photos.

If you do that, you should be able to log into the same Apple ID at www.icloud.com using Chrome and view the photos there.

Note that you cannot view the contents of iCloud Backup at icloud.com -- iCloud Backup and iCloud Photos are not the same thing.