I sympthize about the flies. This year I noticed how many flies I see at various flowering shrubs and plants, along with bees of all kinds. As gardenfish said though, I just learned that many good flies look like bad flies, so if you don't have any housefly problems , maybe you can let them be. Also I don't know which flowering shrubs would guarantee NOT attracting flies along with other pollinators.
https://wimastergardener.org/a....
Just fyi, my Burford holly also gets lots of flies, so if you want to sub, don't get that, and bear that in mind with any holly, I would guess.