Mantine, Gyarados, Dodrio, Mantyke, Doduo, Vullaby, Archen, Archeops, and Hawlucha cannot fly.
Mantine and Mantyke can't fly, unless you count flying in the water as flight. The video below will show you manta rays "flying". It is possible that Game Freak gave them the flying type to reference the behavior
hawlucha can glide, not fly