A deep socket spun in an electric drill and a propane torch ain't fancy but it works.
Annealing is highly likely to improve the success rate of case forming, measured in case life and fewer lost to early splits. You don't have to be perfect, just 'good enough.'
- Start spinning the case and aim the inner, lighter blue part of the flame just below the shoulder / body junction.
- Heat until the part in the flame begins to glow a dull red. Anneal in a mostly dark room so you can see this.
- When the glow begins, dump the case into a catch pan. An disposable aluminum baking pan works. Water isn't required, the case cools quickly and unlike steel, quenching has zero effect on how the brass turns out.
- No need to over do it though the time and temp range is relatively broad. Getting a dull (not bright red) glow indicates you're softening the brass.
- Reaching that dull red glow should take 3-6 seconds. That's slow enough to be controllable. If it happens in 1-2 seconds, try turning the flame down some or holding the case further out of the flame.
The number of cases you lose to trial and error will almost certainly be less than the number lost to early splits caused by the combined stress of un-annealed forming + firing.
I built an induction annealer for under $200 but it's powerful (heats quickly) so a learning curve is involved. IME, flame annealing is a) proven and b) controllable. A ton of different experiences, information and misinformation is on the Interwebs.
This guy is a metallurgical engineer and a shooter, has a series of vids on annealing. Of all the stuff I've seen he has the most sensible approach and info.