The sharpmaker will work fine for maintaining the edge on kitchen knives, but if the knives are very dull it will be slow the first time you sharpen. Most people don't use a soft cutting board in the kitchen the way that they should. Their kitchen knives get severely dull from cutting on ceramic plates, glass trays, and tile counter tops. Even though the blades are thin it takes a long time to restore the edge with a medium grit ceramic hone.
The usual "rod" that comes with a knife set is metal and is called a "steel". It only performs a minor maintenance function of straightening out slight edge folding and dents. If the only sharpening that you have done for an extended period of time is to steel your edges they are probably work-hardened (hard and brittle), a little ragged, and sort of rounded. You will have significant work to do the first time you sharpen them with a hone.
To do it with a standard sharpmaker kit: Select the coarsest rods (the brown, medium grit) and set them in the most nearly verticle set of slots (the 15-degree position) with the rods rotated so that the edges of the stones are inwards (rather than the flats). You start with 15 degrees because you need to thin the edges. It is optional whether you work on one side of the edge at a time or alternate. With the sharpmaker I usually alternate. Do about 20 strokes per side, rotate the stones 1/3 of a revolution and repeat 20 strokes per side on the next set of edges. Rotate another 1/3 turn and repeat with the third edge on each rod. Now for convenience repeat that process doing 20 strokes on each of the flats of the rods. You probably don't have a sharp edge yet. Scrub your rods with sink cleanser and water to remove steel residue clogging the surface. Repeat the above procedure until you get a basically sharp edge on the whole length of the blade. I would guess that thinning the edge might take around a half hour the first time you did it on an old knife (it could take an hour). If you bought the (expensive) diamond hones for your sharpmaker you would be done in about 1/4 the time.
I would use a different hone for thinning the edge on a knife. Kitchen knives are actually easier to sharpen than most other knives, but they are often a lot duller than our fancy toy knives when we start. For a kitchen knife I would get a cheap dual-grit (coarse grit on one side, medium-fine on the other side) aluminum oxide bench hone (it might be called a carborundum hone or India Stone). Aluminum oxide cuts fairly fast and cuts pretty smooth. It is a good choice for blades that are not ultra hard, like kitchen knives. When you are thinning an edge by hand the angle is not critical. Somewhere between 10 and 20 degrees should work. Use the coarse side of the hone for virtually all of your thinning. I sometimes use the edges of a bench hone for faster thinning. You will also want to periodically scrub your hone with sink cleanser. I often work by the sink an just run the hose under the tap (either continuously while I work or periodically to flush the hone).
Once you have your blade thinned, the sharpmaker will keep an excellent edge on the blade with minimum effort. I particularly like the cutting edge I get using the brown rods.