Cruiser squadrons and destroyer flotillas use different command levels

If a vice admiral leads a cruiser squadron, would each accompanying destroyer flotilla be commanded by a rear admiral?

No. Captains normally command the flotillas; a rear admiral appears at a higher divisional or combined light-forces level.

Individual destroyer flotillas would remain under captains when accompanying a cruiser force led by a vice admiral. Even a four-cruiser squadron could have a rear admiral commanding its second division, and the answer expects that additional flag officer in an eight-cruiser squadron. Two destroyer flotillas would not ordinarily justify a separate rear admiral for light forces. The suggested scale is around four or five flotillas, unless a rear admiral is assigned to overall command. The presence of a senior officer in the cruiser squadron therefore does not raise each accompanying flotilla's command rank.