What animal has a long non-flattened naked tail but know how to fly?

The animal you're describing is a monkey.

While most monkeys are arboreal and have prehensile tails, some species, like the proboscis monkey and spider monkey, have long, non-flattened, naked tails that they use for balance and swinging through trees. These tails are not prehensile, meaning they can't grasp things, but they are very strong and flexible.

It's important to note that monkeys cannot fly. They are mammals and therefore do not have wings or the ability to achieve flight.