After reading lots of web-pages which turned out to be American, and therefore misleading, I've gone and put double flares on half my brake unions.
Google for this stuff and all that comes up is "never ever use single flares on cars", "single flares will kill you to death instantly", "not only will this kill you it will hurt the whole time you're dying", "this will kill not just you but also innocent children", etc. etc.
Turns out that what the tool does if you only do the first stage is not that kind of "single flare", also known as the "death flare", but a "bubble flare", which is what you actually need most of the time on a Mini.
Currently my understanding is that I want that dome-shaped end ("bubble flare") on pretty much all the unions. That's what the pipes coming out looked like anyway. The "double flare" is what I want on the female side of a coupler.
Oh well I'm getting plenty of practice with the flaring tool.