How to move iPhone photo album and compress into zip file?

If you mean on an iPhone your cannot do that; the Photo app is a database, not individual files. That is also true on a Mac. You would have to export the photos to a folder or folders on your computer from the photo app or iCloud to convert the photos to individual files, then compress that directory. Although they won’t compress; jpeg is already a compressed format. It will just create a zip file that is slightly larger than the sum of the individual image files due to added metadata and overhead.