From the school of hard knocks (some 35 years of machining and gunsmithing) muzzle flush is the only way to go. Once you use a good muzzle flush system, you will kick yourself all the way to your favorite bar to drown your previous stupidity in chambering without a muzzle flush system. It is far, far superior (higher chambering speed, better finish, less reamer wear, flushes out the chips, much faster) to using the old "brush chips and wipe or squirt oil" method!!!!!
Sorry folks, but you gotta make your own, the systems I have seen for purchase are somewhat junky.
The $100 coolant sump with centrifugal pump that Enco sells is perfect (10 gallons). Do not use a positive displacement pump!!! With the centrifugal, you can put a valve on the discharge to throttle the flow.
I use a high quality (with extreme pressure additives) soluble oil. Regular mix rate is 20 parts water to 1 part oil. I use it 1 part oil to one part water.
Here is the rotary union: It takes up to a 1-1/4" muzzle diameter. Look closely and you will see the copper shim (Made from household copper water piping) wrapped around the barrel at the cathead, another shim is under the rotary union screws. I dial in the union before assembly (it is two parts, one part has the screws for clamping on the barrel, the other part screws into the barrel clamp and has the rotary spindle inside). Also have an extension, for reaching through the headstock when the muzzle is chucked in the 4 jaw chuck and the breech in in the steady. Note the anti rotation pins. The black body is made from moly impregnated nylon, self lubricating, especially with the oil mix inside. Has two O-rings inside for sealing. I gave it 1/2 thou clearance between the inner rotating spindle and the outer body, does not leak a drop. I have posted all this before, do a search!!!
Somewhere I have a photo with the unit disassembled, will try to find it and post.