"Fledge" means to care for a young chick until it is able to fly.
Cuckoos are known for laying their eggs in other birds' nests, expecting the other mother bird to fledge them. Hence they are 'parasitic'.
"The upshot is that crows which raise both their own and cuckoo nestlings to the point when they can fly fledge fewer of their own chicks than do crows which fledge a clutch without cuckoos."
Crows which fledge their own young plus cuckoos (ie. which raise both their own and cuckoo nestlings to the point when they can fly), fledge fewer of their own chicks.