It seems to me that the tail of a whale can itself be referred to as a fluke; or it can be described as consisting of two flukes (one on either side). But I'm not sure you can refer to the tail fins of a whale.
According to animals.mom.me (a site about pets and "other animals"), "So much diversity exists among whale species that some have only the most basic traits in common with others. Flukes are among them. Flukes are the two lobes of the whale tail. While each whale has flukes, flukes themselves differ from species to species. In some whale species, flukes are so distinctive that researchers use them like fingerprints to identify individuals."
It continues: "When a large whale prepares for a deep dive, he arches his back, moving the central part of his body above water to get a better downward angle. The arching gives the whale a humpbacked appearance. With his head in position, he moves downward. The last thing you see of him before he disappears into the depths is his fluke sticking straight up above the water. Called fluking, this diving posture gives researchers a good look at the tail markings, which can be distinct enough to identify individual whales. Some whales, notably fin whales and minke whales, don't fluke."
Note that in this second passage, the whale has only one fluke; whereas in the first it has two.
The fin whale is the second largest species of whale, after the blue whale.
Wikipedia is somewhat lacking in clarity on this subject: whales, it says, "have a cartilaginous fluke at the end of their tails that is used for propulsion. The fluke is set horizontally on the body, unlike fish, which have vertical tails."
I'm not convinced that the flukes are at the end of the tail. As I said at the start of this note, it seems to me that you can either call the tail a fluke, or else the tail consists pretty much of a pair of flukes. If a whale has two flukes, they are set horizontally.
Do whales do have fins? Over to reference.com: "Some whales have fins, but not all species do. Some types of whales have dorsal fins similar to a dolphin's that help them to swim.
"The main purpose of a dorsal fin is to keep the whale stable as it moves through the water. It also prevents the whale from rolling around in the water while it moves. While not all whales have dorsal fins, all whales are born with two flippers along the sides of their bodies that help them to propel their large bodies through currents in the ocean water with ease. Beluga whales and baleen whales have dorsal fins."
No mention of a tail fin though ...
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