Flipper (like fluke) is more restricted than fin, which ODO defines as
A flattened appendage on various parts of the body of many aquatic vertebrates, including fish and cetaceans, and some invertebrates, used for propelling, steering, and balancing.
as opposed to flipper,
A broad flat limb without fingers, used for swimming by various sea animals such as seals, whales, and turtles.
The terms flipper and fluke are almost never used to describe parts of fish, even when the appendages are fleshy, as with shark fins, or lobed, as with lungfish, which indeed are known as lobe-finned fish.
For cetaceans, many people use fin and flipper interchangeably, but in more formal discussions of anatomy, references to dorsal fins, pectoral flippers, and tail flukes are most common. Dorsal flippers is far rarer, not turning up at all in a Google Ngram search. Pectoral fins appears to be similarly rare in reference to mammals, although this is difficult to establish, as fish do have pectoral fins, and not only fish but aircraft and Cadillacs have tail fins as well.