I will second this with my clarinet lol. if you have a music shop, you should be able to find one of these, one for a clarinet would be better though, a bit smaller.
I just cup the end in my hand and hold it up tight to the faucet and let the water blast everything out. Seems to work just fine although I'd imagine there is still gunky stuff in there that a cloth or brush would get out. However, in my opinion, the water blasting through there works just fine and prevents clogging.
Another idea. I bought a venturi tube cleaner. Venturi tubes are used on gas BBQ's. The brush is mounted on a springy shaft and the end is same as any bottle brush. The beauty of this type of brush is that it bends in any direction, such as for a U tube. Should be able to pick one up at any hardware store, appliance parts supplier or in the appliance section of a department store.
I used to put some rice in the tube, add some water, and shake shake shake!! It works fairly well but you have to be careful not to get rice stuck. Really brings out the gunk.