First, your image you are separating should be a minimum of 300 PPI (Pixels per inch)at the finished print size. (I know most folks use DPI to express this, but that's just a pet peeve of mine.)
OK, once you have the three channels, each one has to be saved as a spot color. To do that, double click the first channel; in the ensuing dialog box, check Spot Color; click on the colored box, you'll get the Color Picker; click the Custom button, pick an appropriate PMS color for the channel you picked, and click OK.
Do that for each of your 3 channels that you've created. (Keep the RGB channels intact as well, as that will look better when you place it in Illustrator to print.) Now save the file as a DCS 2.0 format. Done.
Next, Place the file in a new Illustrator document; when you do this, you will see the file cleanly (that's the RGB channels) and the 3 Spot Color channels you created will be added to your color pallet. In the options of your color pallet, in the upper right hand corner, choose "Select all unused colors" and then delete them; this will clean up your color pallet nicely. Go to print, select your printer and page size, then click on Output, shut off all colors except the 3 channels you want to print, and you're off!
Steve
Though you could trace, it will look much better if you don't. Tracing does an inefficient job on small things like texture, and you lose the "organic" look of the texture.
