This isn't quite as practical for rifles lacking the Hawken hook breech and wedge keys.
But my rifle does.
So I remove the barrel assembly
Most hand held showers have a hose that will screw onto male 1/2 in straight pipe
By whatever plumbing miracle you can figure out,you want t attach that hose to a length of approx 3/8 diameter brass tubing..The length of the tubing is at least muzzle to breech plug.
On the end of this contraption where the hose connects,I attach a piece of wire. I used aircraft safety wire.
I slide that all the way into the barrel.
I attach the wire to a ramrod thimble to hold the tube in the bore.
Then I just turn on the hot water.The water jets full pressure into the breech plug and everything flushes out the muzzle. Soon,the water will run clear.
Hopefully,your water will still be running hot.
Use patches to swab and dry your barrel,then oil it
If I'm someplace other then home,I use hawgs method of sticking the breech in the billy pot,and pumping.