I personally haven't tried the Omnia with a REDFLY, but I've heard from our testing dept that the main problem right now is with the Omnia's custom Today Screen (many of the core apps work just fine).
You could try installing any 6.1 driver (make sure it's one for a phone with a touch screen like the Treo Pro or Tilt) from the normal install page at
http://www.celiocorp.com/install/ or it would most likely work a bit better if you installed the latest build of the Touch Pro/Diamond/Xperia beta located at
http://www.celiocorp.com/install/beta/
You can always uninstall the driver from the phone if it causes problems. We haven't ever truly bricked a phone with the REDFLY driver, but it's always a good idea to make sure you are backed up in case you have to do a hard reset (not common but could happen with a beta driver).
Keep checking that
http://www.celiocorp.com/install/beta/ page for a mention of the Omnia because once it is listed there, the driver posted will work much better (a true beta).