This is the last step! In this picture I have two of the three rings wrapped around the shaft in a stepped and alternated order. You must be sure to offset the rings butt joints 1/3, 1/3, 1/3 for a three ring box or 1/2 & 1/2 or said another way 12 o'clock and 6 o'clock for a two ring box.
It's also perfectly fine to wrap one ring at a time and push the nut over it BUT WITHOUT TURNING IT until you get all three rings into the nut and staggered. It's best when using this method of "stuffing rings" to mark the outside of the nut with a Sharpie marker where the joints are and then when all rings are in the nut, and staggered, you can finally thread the nut onto the box.
I custom made my own tool for this & it has a similar thickness to the flax for "stuffing the nut" (see the "tool" below). I don't advise the use of a pick to stuff the flax into the nut as this can cause significant unlaying or twisting of the flax especially with GTU. When ever possible try to get at least three rings of packing in your stuffing box as most are designed for at least three. Some nuts can actually fit four & if so go for it but make sure you have enough threads to get a good hold for the female nut.
One more very important note is that you really need to use the correct size packing. Going one size to big can eventually wear a groove in the shaft and one size to small will never seal properly. Please use due diligence to determine the proper packing size for your particular stuffing box.