Silent Partner is really the only way to fly roped solo free climbing.
The SP is no doubt the 'safest' way to go so long as you don't use it in cold weather, but there is no flying with an SP. Rather, it is in fact quite slow to use compared to an Edelrid Eddy with the rope in a backpack as mcreel verifies.
[ Note to anyone interested: after trying many different ropes with the Eddy over the years since it first came out, I've settled on the 9.9mm NE Glider as more or less optimal for use with it. I also run the rope through a velcro-ed 'tube' about double the diameter of the rope on my shoulder strap which lets the rope run smoothly when I pull it, but stops the rope up short in falls. YMMV. ]