A .22 RF barrel doesn't need to be cleaned very often. I agree with Ledbetter, every 1,000rds is enough. This goes against the indoctrination many of us received in military training or from our father's knee - every time you shoot, if it's 10 rounds or 100, disassemble the firearm to it's component molecules and clean the hell out of every thing till it's spotless.
Some would argue that you never need to put a brush down a .22 barrel because velocities are to low to cause a significant plating of lead or jacket material. In fact, some of the worlds most accurate .22 RF target rifles have never had their barrels cleaned, even though they've fired tens of thousands of rounds.
As stated earlier, the real danger is from the damage that can be caused by over-zealous cleaning. Anyone who's looked at the rifling near the muzzle from a sample of old service grade M1 Garands can plainly see the damage ritualistic cleaning can cause.
The barrels on my .22s never see a brush. My practice is after shooting to use an old tooth brush to apply a little oil (I use CLP) to every thing and run a oiled patch down the barrel to prevent surface rust, as required use a brake cleaner type product to blast the gunk from the action to keep it functioning reliably (frequency is very dependent on the type of ammo you shoot but is typically every 500 to 1,000 rds), and occasionally (like every couple of bricks of ammo) use a little Hoppes on a patch - that's it. -- Kernel