This is a very minor disagreement about a most likely very modest gain in chain life, even if I'm right. But we can define the likely gain a bit further:
The roller, as its name implies, in the end is likely to be worn the same amount all round, so flipping the chain will not necessarily affect its contribution to chain life except marginally, as I will explain below.
But the bearings in a never-flipped chain are worn on three sides only, because that is where they bear load as chain ramps up and off the teeth on the gears. On the outside of the chain (horizontal flat surface pointing at the sky and the ground) the bearings bear no load and wear only in relation to the dirt that clumsy oiling (on both sides of the rollers, so creating an air lock for the dirt inside) or no oiling has left in between the roller and the bearings.
So the marginal gain to "standard practice life" (not flipping the chain) that flipping the chain will add is a variable feast depending on when the chain is flipped. In any event, it cannot ever be greater than one third of (at a first approximation) one half of SPL, because three of the four 90 degree sides of the bearings are already worn when the chain is flipped, and two of them will wear further even as the fourth side wears down. This identifies the maximum theoretical gain with one flip as 16.666 percent. I'll explain below why the gain could be much smaller.
One can however escape this limiting condition by regularly flipping the chain, so that all the bearings wear down smoothly, in which case a gain of 33.333 percent is the theoretical maximum; see below about complicating factors leading to a likely much smaller gain. Explanation follows:
Remember that chain wear is measured cumulatively on the edges of the bearings aligned vertically, whereas we are now talking about slowing total chain wear by bringing in a second horizontal edge, where previously only one horizontal side of the bearing was in full use.
So what we have to determine is how much bringing the second horizontal side into play will slow down wear on the two vertical bearing sides. It seems to me that some slowing will occur because, from the roller's viewpoint, the bearing is now ovoid rather than asymmetrically round, and thus, until the roller wears down the new surface of the bearing presented to load, the sides over which we will measure elongation will wear somewhat slower.
Taking a wild guess <tm>, I'd say that with one flip of the chain during its life, the gain could be between 3 and 5 percent, and with many flips possibly double that. That is also a hint that any experiment had better be done by a high-miler and quite carefully controlled because we're working with relatively small fractions of total mileage.
Unfortunately, that's not all that cerebration leads us to:
It may also be the case that flipping the chain, especially flipping it only once when the bearings are half worn on three sides, disturbs the roller which previously rotated in harmony with the incremental wear on the bearings, or that the new bearing surface even gouges the roller, in which case the longevity gain on the chain will be negative (a euphemism for "fewer miles per chain").
