After flagging one or more images, "Undo Flag as Pick" appears at the top of the undo stack (Edit menu, now the Ctrl-Z action). Lightroom flashes the syncing icon briefly, and the flags sync as expected to Lightroom Classic on another machine. Contrary to expectation, opting to undo the flag action neither removes the flag in Lightroom nor syncs any change in flag status to the cloud, however. The flag action is popped from the undo stack, and the next "undo" action will be the previous action, for example "Undo Change Selection." Same problem with undoing a "remove flag" action. I have not tested comprehenbsively but actions unrelated to flagging seem to "undo" as expected.
Actively setting the flag off works and syncs as expected.