Well, maybe not *key*, but this is the way I do mine. I use a peanut butter jar with a tight-fitting lid. The chain goes in and about a half cup of kerosene is added. Lid tightened; shaken vigorously. Depending on how much sediment I see, I may lift the chain out, drain the jar into a "settling" container, wipe out any residual sediment. Once the sediment is gone, I'll use a couple more rinses with fresh (or recycled) kerosene. The chain is then hung up to drain for a while, preferably overnight. The kerosene used is allowed to settle for a few days, then the clear (if colored) supernatant is decanted off for future use. It can be re-used this way many times.

Why kerosene? It's readily available, inexpensive, relatively non-toxic and much less flammable (and therefore safer) than gasoline. Another acceptable choice IMO is WD-40 (I have a gallon can of the stuff!), but I prefer kerosene.

I've never seen residue that requires scrubbing over and above the shaking. When the chain is shaken, there is contact with other chain links which may substitute for scrubbing.

I don't want to rain on anyone's parade, but I don't like the idea of wire-wheeling the chain. For one thing, that will aerosolize the solvent and debris; a mask should be worn in addition to the recommended safety glasses. It might also be a finger-snagging hazard. For another, it must make a hell of a mess. The wire wheel will only clean the side plates; it can't get between the moving parts or into the spaces for the cogs (note the correct use of "cogs" ). The chain may look better, but the outsides of the side plates are not involved in wear processes of the chain or sprockets.
Steve