Making the comb is the (relatively) easy part, keeping in mind SmokeyJoe's tolerance value (1/1000th inch). Several good craftsmen make combs from a variety of materials. Covers are also (relatively) easy to do, but harder than combs, PROVIDED you know how to shape the curvature. Reedplates are harder to do, (tighter tolerance) and reeds are plain out HARD to do. (Smokey Joe is THE EXPERT on making reeds from a variety of other things.) The mensurs (length, width and especially the varying thickness from reed pad [base] to the tip of the reed) vary considerably with each individual reed.
I had the pleasure of helping (in a very minor way with some program code) Vern Smith on a reed making machine he designed. It proved (eventually) unworkable. Everything went fine until the final few passes across the reed surface to mill in the mensurs. The problem: the blade would "grab" the very thin metal and cause it to bend or break. AFAIK, Vern never got that bug worked out.
An alternative is to get the reedplates made by a machinist and then use commercially avalable reeds, focusing your homebrew efforts on the comb and covers. Seydel offers all of their stainless steel reeds for their harmonicas. The Seydel Harp Configurator allows you to pick the reed pitch (within a certain range, usually about 10 half tones) for a given hole and breath direction. (Actually, the breath direction is irrelevant; the same range of pitches is available for both blow and draw reeds.)
I can tell you for a fact (personal experience): it ain't nearly as cheap nor as precise as a commercially produced harmonica. Getting all the little details correct is not an easy process.
I have a design for a slideless valveless 4.5 octave chromatic. The drawings spread over 42 pages, with lots of fine details. I had Will Wu, a Chinese harmonica machinist working as Will's Make, make everything except the reeds. Will has very reasonable prices for his work, and I can tell you, he's a superb craftsman.
So far, I've spent $1600 on it - and it's not functional yet. (That's MY problem, nothing to do with Will.) Will did outstanding machine work, and also made several suggestions for making the machining process easier, suggestions which I readily accepted. The reedplates were lazer-cut in one of the big Chinese harmonica factories. Will made the comb (silver-plated brass) and the covers (machined ABS plastic).
If you have an unlimited amount of time AND the machine tools AND the skills (or the desire to learn the skills), then count the cost and go for it!
Whatever floats your boat and fits your budget - some people are satisfied to build a rowboat; some people have to have their own homebuilt yacht.
Crazy (there's a good reason for THAT nickname!) Bob