In order to avoid the stripes, I suggest the following:
Create the map in really high resolution 4000x4000 or even more.
Apply a little gausian blur when it's done to smooth it more.
In brush settings adjust spacing to minimum.
Tip: You can try the Liquify filter to create these flares, although it's not exactly the desired result but it might be useful.
In general the problem is that the map is a raster and 3d works with vectors. For example in cinema4d the default cube is 2x2 meters. If you calculate that screen resolution is 72 pixels per inch, this means 72/25.4mm = 2.83 points of data per millimetre. 2 meters is 2000 millimetres * 2.83 = 5669px, therefore if you want high quality displacement you would go for 6000x6000 map.
Actually just now I tried to find a better way as I might need this too. I went to Illustrator. I drew a curvy line with the pen tool. Then I used the Width Tool to widen some parts of the path. You can also widen only one side by holding Alt. Then I set the outline type to gradient and here we go. I think it's a perfect solution.
The coolest thing it is fully parametric. The curve can be changed. The flare sizes can be changed. The gradient "slope" can also be changed. Have fun with it.