The interactions with lilariah are weird, yes the intended behaviour is that all angels always have flying as long as she's on the field, but is it intended that if you use drag down on an angel card that has flying by default while lilariah is on the field nothing seems to happen, but then when lilariah is moved to support that card loses it's flying?
I think what's going on is that the cards have a default value for whether it's flying or not, with drag down changing that value, while lilariah's effect completely overrides/ignores that value.
Whether flying actually 'stacks' with lilariah or not, I don't know, I only have one lilariah to test with, if someone could test with multiple lilariahs on the field that'd be helpful.
Have a couple angel cards that have flying by default on the field, play lilariah, kill lilariah, play another lilariah, awaken first lilariah, have both on the field, use a drag down on flying card 1, move both lilariahs to support, does card 1 lose flying? if yes then I think my hypothesis is true, if not, put both lilariahs back in the field, use 2 drag downs on flying card 2, move both lilariahs to support, does card 2 lose flying? if yes it's probably stacking.
(Could even try with 3 lilariahs, eg if you use 2-3 drag downs on a card while there's 3 lilariahs)