The term 'flow' is a better translation than 'style'. The idea in using the term (as in Jigen Ryu or Kashima Shinryu) is that information 'flows' from the headmaster to the students, and thus transmission of martial skill and lore is likened to the flow of water from a high place to lower places.
It's more complex than that, but that's the idea.
I think Jun's got some .wav files of common aikido and budo terms on here somewhere, dunno if ryu's in there. The Japanese r's 'flipped', and sounds like a blend of 'r' and 'l'; 'yu' is as it looks, but a bit clipped at the end.