Roots can only absorb oxygen when they are wet.
When they are fully submerged in water, you have to make sure that there is plenty of DO in that water. (DWC or waterfalls for example)
Getting maximum DO is very, very easy. Just stirring your water every hour could be enough. Even the Kratky method works, so people make a big fuzz out of it. Often totally unnecessary.
When they are not fully submerged in water the whole time (soil, cocos, rockwool) they will absorb the oxygen in gaseous state. Not directly however. The roots are wet (a thin layer of moist) and the oxygen in gaseous state hits this thin layer of water and turns into Dissolved Oxygen.
With FD you use both technics: When the water floods in, there is plenty of DO available: because of the movement of the water. So it doesn't really matter that much if you flood for 5, 15 or 30 minutes. Plenty of DO all the time.
When the water drains, the roots (and the clayballs in your set up) stay wet for a while and there is plenty of oxygen in gaseous state.
Roots can stay dry for a while; this does not automatically cause problems.
Even if you would have no medium, so just a netpot with a collar, they will grow fine. Also if there is plenty of time in between your cycles.