So on the flute side of things, if I remember correctly from around that era, he’s using an omni lapel wireless mic inserted into the bottom of the flute (you can see the cable coming out of it and the wireless pack on his hip). That’s then running into a volume pedal and finally into a tiny practice guitar amp with built in distortion.
Because of the nature of the flute he has a lot of control over the feedback “pitch” by changing the position of the flute (and his body) to the amp, along with his mouth/embouchure. The volume pedal also helps a lot there. (you can see some of it in more detail in this video I think) (also I highly recommend his album Amp/Al which has more of his explorations on it, along with a studio version of this piece (and brilliant artwork by @Angela))
The mic, wireless system, and amp, are all pretty shit quality, which adds to the sound of it too, particularly the wireless system as in quieter sections you can hear the sputtering/downsample-y sounding AM of the thresholding being crossed.
For the snare I’m also using an omni lapel mic, which happens to be a Naiant X-X microphone because it was cheap and turns out pretty good sounding. (I own like 5 of these now! (and at some point I’ll probably pick up an LOM mic to test/compare with)) It runs into distortion (in Max), then out into a volume pedal and finally a guitar amp (a 1x12 Fender Reverb in that performance). (these days I go until a full-range wedge and put some filtering on the input to avoid having bass or highs runaway with the feedback, but I find it’s more dynamic and expressive)
If you’re interested in this piece/approach I go into a LOT of detail in this blog post here:
As far as more general advice, I highly recommend the book Getting a Bigger Sound, as it covers a lot of ground about different approaches to amplification (great section on contact mics for example). But besides that I’m a big fan of omni mics for this kind of thing, as you get a fairly realistic signal into the computer. If it’s in your budget DPA 4060s are pure magic. I bought a pair of those as soon as I could afford them and it made a massive night and day difference. Particularly for drums, I can honestly get a really solid and full sound by just clipping it to the front of the snare. (Going with the 4060s was inspired by early jams with @tremblap, who is often my “fancy gear mentor”).
Going with omnis obviously brings in problems with room noise, bleed, etc… so that’s not going to be the best solution always, but it works well for me.
As far as contact mics go, I’ve been suuuper happy with K&K hotspots, which are cheap and pretty full sounding. As a point of reference I also own an expensive Schertler, which is worlds quieter, but not quite as full ranged as the K&K. In either case a preamp comes in handy. Lots of DIY options available there. In terms of the mic itself, unless you get some good elements and/or know what you’re doing, I wouldn’t go DIY here as they tend to sound shit and are quite noisy, and things like the K&K are pretty cheap.
Hope that helps a bit (and happy to answer any more specific questions).