Flax, once harvested, must be soaked in water to process it further. This soaking helps to separate the fibers from the less useful parts of the plant. The byproducts of rotten flax eventually become some of the most fundamental items in Egypt, such as rope and canvas.
In order to rot flax, you must have the flax processing skill; some flax, of course (harvested flax, not flax seeds); and be standing near a body of water. In your "Skills..." submenu, you will find a "Rot flax in the water" option. Once you have selected the number of flax to rot, a buoy belonging to you will appear with a red flag.
It takes 5 TeppyMinutes to rot flax. Once your flax has rotted, the buoy's flag will change color to white, at which time you can pick up your rotten flax.
Alternatively, flax may be rotted in a tub; however, since tubs crumble with use, this is never done in practice, except when there is no water source nearby.