First, don't buy those syringes with the protective coating. It's shellac or lacquer or something which alcohol will dissolve and make a sticky mess. (Guess how I know!) If you have, take a piece of religious (holey) tee-shirt, saturate it with isopropyl alcohol and scrub off the spray shellac or lacquer or whatever it is.
Second, pour about five fluid ounces of 91% isopropyl alcohol into a glass made out of glass. (Isopropyl alcohol will affect some plastics.)
Third, jam your carto into one of the two tubes that come with the kit. You jam echo-e's on via the mouthpiece end. It will fit -- you just have to be firm with it. Then attach the other end to the syringe.
Fourth, pull out the syringe plunger to suck the isopropyl alcohol through the carto, then push it back in to expel the alcohol back into the glass. Do this slowly, lest the assembly fall apart and spray alcohol all over the place. I do about 15 cycles of this out-then-in process, but that may be overkill. It's amazing how much gradoo you get out of the carto! Replace the alcohol every couple of cartos or when the alcohol changes color considerably. Experience will tell you when to do this.
Fifth, take the carto off the tube and inspect. The filler should look grayishly wet and not any other color.
Sixth, let the carto dry for a day, or sling it, battery end down, to remove most of the isopropyl alcohol. Inspect the filler again. Once you've dried it on the surface, the filler should be fluffy white, just like it looked when it was brand-new. Use a brand-new carto to compare. Also smell the filler. If the filler isn't fluffy white and/or you can still smell flavor, repeat steps three through six again.
Seventh, let the carto dry for a week to be certain all the isopropyl alcohol has evaporated. Vaping a droplet of isopropyl alcohol probably won't kill you or make you go blind, but it is profoundly nasty stuff and will ruin your new charge of eliquid. Needless to say, during the weeklong drying process, you're using another bunch of echo-e cartos.
Also, be sure to wipe the exterior of the carto and don't let it air-dry: isopropyl alcohol can cause the black paint to de-adhere. I found this out the hard way. If this does happen to you, though, all is not lost. Take a toothpick and scrape off the paint. The unpainted body of the carto is a nice brushed stainless steel which looks great on steel colored batteries and normal on most other battery colors.
Right now I'm using two sets of five echo-e cartos each. One set is in use for a week; the other set has been cleaned and is drying. The whole cleaning process takes about ten minutes for a set of five cartos. It's a Saturday morning chore which is worth doing: those cartos cost about $5.00 each. The set currently drying has been through this process six times. I haven't had to pitch an echo-e carto yet.
Hope all this helps!