What class do Flounder belong to?

Flounders belong to the Actinoterygii class

The Actinopterygii (the plural form of Actinopterygius) constitute the class of the ray-finned fishes.

The ray-finned fishes are so called because they possess lepidotrichia or "fin rays", their fins being webs of skin supported by bony or horny spines ("rays"), as opposed to the fleshy, lobed fins that characterize the class Sarcopterygii which also, however, possess lepidotrichia.