I've heard that whales do not have the breathe reflex that humans have. Is this true?

I'm not sure what you mean by "breathe reflex". Whales, like all mammals including humans, must breathe air and can do so without conscious effort (i.e. reflexively). Whales and other aquatic mammals can hold their breath for much longer than humans which allows them to stay underwater for long periods of time but eventually they must return to the surface to take another breath.