Do you really need to go down what can turn out to be a very deep and expensive rabbit hole? A milling machine needs to be equipped, even for simple jobs. You'll need work-holding equipment (vice, clamps, etc.), work setting equipment (parallels, V-blocks, edge finder, etc.), drill bits and milling cutters (so many choices…), chucks, metrology equipment, and so on and so on. And then you'll need the background information about cutting speeds and feeds, and so on. You'll also need to accept the limitations – or take steps to overcome them – of a little machine that may not be the best engineered…
Thin sections of soft metals can be easily worked by hand, and accuracy can be aided by the use of improvised jigs and fixtures. Files are wonderful things, but you've got to be prepared to buy the correct ones for your application(s) and preferred way of working. Buy good makes (eg Grobet, Vallorbe), and you'll wince at the price, but they're well worth it.
I would think that most accordion reeds start as blanks, punched from spring steel sheet or strip. This would allow the wider part around the rivet hole to be formed at the same time as the thinner vibrating part., and all pretty much free from distortion. The desirable 'hand-made' reeds start as a strip, the same width as the part around the rivet hole. Their characteristic blue edge beside the rivet hole is the blue edge of the parent strip stock. In these reeds, I don't think the tongues could be punched to width, so perhaps the tongues are, in all cases, formed entirely by machining. The apertures in the reed plates are, I believe, broached. And then an old gaffer in a ramshackle Italian cottage-factory got to work with files (or a filing machine if they were flush) and abrasive belt sanders. Or you could buy them… Stick 'Carini de.na.' into your search engine: I can't remember whether bare tongues are available from there, but everything else is.