To be qualify as a line-out, the signal needs to be on line level. What that means, at least on my understanding, is that the dynamic range of the signal must be at its best (and over a certain voltage). Best dynamic range is just a way of saying the output signal is at its maximum before distortion starts to increase due to over-stressing the circuit. In short, you get the cleanest, best possible SNR on the line-out, which makes it the best option for amplification. Due to the fact that headphone-out can be variable (which means its dynamic range / SNR isn't always at its best), amping is less ideal - thus why if you want to amp the headphone-out (HO), you should keep the volume high but make sure you don't hear any distortion. That way you get the best possible dynamic range from the HO, though it is most likely not going to be as good as a real dedicated line-out. BTW, some people like to call it a 'virtual line-out', but hmm...
IIRC, on the case of S:Flo2 (dual WM8740, and actually on some DAC chips), the DAC chips themselves do not output your regular analog signal directly, thus you will need an opamp to 'convert' the signal, and that is why the opamp is there for. Some time the amp is there to amp the signal to line level as well. In some case, especially on SoC (System-on-Chip), the DAC output line-level signal and you don't need an extra opamp. Technically you can say it is double amping - but it is double amping on line-level signal, which usually doesn't deteriorate the SNR like amping HO.
Also, it is usually better not to pair two of the same opamp if you know which opamp is on the line-out. Though you are amping a line level signal, there is no way to avoid the sound signature of each opamp in the signal path. If there is two in a chain, the sound signature will likely to be exaggerated. For example, if there is an AD8620 on the line-out, you will be better off not using Corda MOVE (which is dual AD8610, the mono version of AD8620). In theory anyway.