Is there a quick way (flag? identifier?) to select all of her photos on my phone and delete them?
Not that I am aware of. How do you separate a single jar of sand created from 2 jars of sand?
Once downloaded, you may be able to look at the phone that created the photo and separate them. You won't like this answer, but iPhones are designed to be used by a single user. When multiple devices using the same Apple ID sign in to iCloud, all photos from all devices are loaded on to the camera roll.
iCloud and the iOS Photos app don't display metadata that you could use to separate photos by device used to create.
Your idea of downloading to a "neutral" place strikes me as untenable (because we would have to sift through about 10,000 photos and videos) unless the iCloud archive itself has a flag which tells us from which device the photo originated.
Be that as it may. It is really your only option using Apple's tools. iCloud Photos is by no means full featured and does not use metadata. It is a convenient way to view your photos. iOS Photos is also feature impaired.
You may want to look for a 3rd party photo management app for iOS that can analyze your library and cull "her" from "you"