Sterling silver is easy to use for keys and is widely available through jewelry suppliers. I make my own keys through processes such as fusing, cold forging, cutting to shape, filing to refine the shape and then finishing. I prefer forged keys over cast as these can be bent and re-bent as needed, to tweak them into perfect functioning. For springs I use off the shelf wind instrument springs from band instrument suppliers.
Tubing is harder to source. A large band instrument supply house or sometimes your local repairman has several sizes of tuning slide tubing used on brass instruments. I look for the closest size available, and then press it through home-made dies to size it to the diameters I need. I use brass inner and nickel outer slides mostly.
Gun drills are available through Drillmasters - see http://www.drillmasterseldorado.com/
Gun drills are something you can make also with drill rod. The FOMRHI journal which you would find at a university music library has several articles on making these
Reamers you should learn to make yourself. FOMRHI again has articles on this.
My earliest reamers were made by turning a piece of round steel on a wood lathe at the slowest speed, and simply filing it to the taper I wanted, and polishing it with emory cloth. The reamer then was cut up the middle with a hacksaw. This took several days to do and seemed like it took forever - but it was good discipline. I was a bit inspired my my dad’s tales of early machining school where one of the first assignments was to transform a rough lump of cast iron into a perfect cube using only a file, vise and square. Took most of the students a month! So a week to make an important tool didn’t seem too bad.
These days I use “Stressproof” steel for my reamers - its actually just 1045 Carbon Steel (.45% carbon) which is available at steel warehouses. Drill rod can also be used but is harder to work. The reamers are not hardened afterwards. I use Myford metal lathes in my workshop instead of a wood lathe so these are turned the way all metal is turned usually. Approximately 1/4 of the diameter is milled away on my milling machine for a cutting flute. The cutting edge is ground, honed and then burnished to an edge.
In a pinch reamers can also be fashioned out of a hard wood such as rock maple, turned and then cut to 1/2 or 3/4 profile. A cutting edge is attached with screws and glue, such as a thin hacksaw blade. One of the FOMRHI articles describes how to do this.
Finally you need to look at some flutes that you would like to copy - and make inside and outside measurements of them. There are museum collections that have been measured, and make these measurements available. Also instruments owned by friendly players. Its best to find something that plays well in some player’s hands and measure that rather than copy something in a museum. Another thing several makers do is to purchase some instruments themselves to then use these as templates for their work. I couldn’t afford this myself - but fortunately I had access to some great Pratten, Rudall and Prowse flutes early on. I have several volumes of notebooks with dimensions. These days I set aside good examples of my work and use these as my templates out in the workshop. Its also great to have these to show the occasional visiting player.