Reading @Thunderforge's answer to this question, I percieved an assumption he had taken on how Hawkgirl and Hawkman reincarnate (which he confirmed in this comment) and that I originally shared:
"a new child from new parents"
Further contemplation however made me realise that if that were true, than we would run into a huge timeline problem:
It is stated (both in the Arrow/Flash crossover and on Legends of Tomorrow) that
- the cycle of reincarnations started 4000 years ago
- they have - so far - been killed 206 times (or 205 if we exclude the first death, when they were already adults).
That would mean that - on average - they would henceforce have to be killed every 19.5 years (or, if their souls jump into genetically identical (!!!) babies the moment they die, at the age of 19.5 years).
We know Savage tracks them when they, or rather especially when Hawkgirl "emerges", in order to kill them. We also know that they had
a child, the late Professor Boardman, who was 10 when they were killed,
forcing them to be in their mid-20s, at least, at the time of their deaths.
For that to happen, Savage would have had to kill them as children numerous times, which would however not leave them with enough time to grow up, "emerge" and meet in the first place. But they have to "emerge", before Savage can salvage their "lifeforce" (or whatever it is he sucks out of their faces) and/or detect them.
- Is our assumption on how reincarnation takes place wrong, in that maybe they reincarnate into an already adult body (if they magically inhabit a genetically identical baby they can just as easily inhabit a genetically identical adult), and the fact that they remember a childhood is just part of the magic but never actually happened?
- Or did the writers really not think that one through, and should rather have said 106 or 156 instead of 206 reincarnations?
Answers on how this works in the comics are also welcome, if there is nothing provided by the showrunners.