To begin w, it does sound like your tire is pretty smooth. You may want to look for another one. Next, do a search for 'Gorilla Grip' it's a tacky towel that's also used in baseball or golf (presumably for gripping the bat/club) and will give you just a bit of stickiness on your forearms, biceps and shoulders to help w the flip.
Finally, make sure that most fo the lifting isn't being done w your hands. That's a good way to tear a bicep. It's frustating when it seems like there's nowhere to put your hands, or when you can't get traction with them, but too many guys try to grab a tire like theyre trying to get a handle on it