I would keep the compost.
Pests thrive only when conditions suit them. It’s not the compost or kale per se, but their state and condition. Maybe your compost is soggy, or too dry. Hard to say.
Whatever, I would use it, and exposure to air + weather will improve the compost, reduce flies.
Add some extra compost so that all soil is well covered, then health of soil is going to improve, so your plants will grow more healthily and aphids have less reason to be there.
A few pests are always present, but I reckon your main problem will become manageable, through health of soil and plants.
