As @sublimeartistry pointed out resistance is a poor indicator of turns ratio because of wire size, but inductance of each winding should be at least in the ball park for turns ratio and from there measuring with the desired signal at the frequency that you want to use is the real world test that works.
This one is a possibility, it looks to be about a 62/1 turns ratio which means you would get 375V out with 6V in from an oscillator drive circuit (I’m not sure what the circuit you have will do, it appears to be different than just the turns ratio, as it says it uses self inductance which I don’t know how to calculate). Primary winding insulation may also be an issue as I expect it is probably 100V as most of the transistor ones seem to be and 400V may cause arc over in the primary as the insulation fails. As you note finding transformers is getting more and more difficult, I guess they aren’t popular because of cost and the various switching regulators now available, but it is a pain when you need one.
You are likely to find that this doesn’t generate enough current to charge the capacitors in any reasonable time which may be an issue in this application. For a camera a 30 second recharge time isn’t an issue because you typically don’t take photos that fast, for a strobe I expect (but don’t know for sure) you need a quicker recharge cycle to be ready to flash at each trigger. If you can’t, you may get timing variation depending on how many triggers occur between recharges (which since the two are unrelated will vary with time). Given that as far as I can see this project is aimed at possibly non electronics people, hand built strobe lights present a danger. As noted earlier a charged 400V cap can present a life threatening danger if you aren’t used to dealing with them (such as shorting them out with a clip lead before working near them to avoid shocks) which may be a liability issue. If you can get enough brightness to be usable, I think the LED solution is more likely to be more cost effective with much less danger.
Peter