Some airplane designs will not flat spin for love or money. A long wingspan and a short tail and small verticle fin i.e. WWI scale models, Cubs, etc. are most likely to flat spin.
When transitioning from a flat spin to a normal spin, the spin rate will speed up due to conservation of agular momentum, the same reason an ice skater's spin speeds up when they pull their arms in.
A search on the subject of flat spins will probably yield a lot more info on the physics involved somewhere in the aerodynamics forum.