My guess is that it isn't too involved on the tax front. Someone please correct me if the following is bogus...
Donate your lowest cost basis stock and write off at current market value. Donate stock directly to avoid taxes incurred by selling. Lowest cost basis because that removes the largest unrealized capital gains from your personal portfolio. Maybe do so over some number of days to cost average if you are donating oodles like Buffet.
There are a lot of nuances missing here. Estate freezes, transfers, nested partnerships, different HoldCos, etc.
Buffett seems proud of his simplicity, so I doubt his structure is too convoluted (bad for his brand to be trying to avoid taxes this way), for people with a small percentage of his wealth all the way up to other billionaires with his wealth have extremely complicated structures that boggle the mind and keep PwC, EY, and similar employed.
The process itself probably doesn't have to be that complicated (or at least it's well understood) but at least the timing is presumably taking tax effects into account.
Even for much much smaller amounts, donations (of various kinds) of appreciated assets can use tax law to considerable advantage.
Donate your lowest cost basis stock and write off at current market value. Donate stock directly to avoid taxes incurred by selling. Lowest cost basis because that removes the largest unrealized capital gains from your personal portfolio. Maybe do so over some number of days to cost average if you are donating oodles like Buffet.