Here is my adventure when trying to do this.
As you can see I started off with a goldish colored cover with darker corners. I guess this is from using the case.
I tried to do Royal Blue like platin465. But it came out as a light purplish color. I did not like that so I out the dye back on the stove at 2-3. and added a bit more dye. (I was using the powdered dye). After 10-15 more minutes with the stove on it adsorbed all the dye that it could. I also noticed dye clumping around the lenses. I used more dye that the water could dissolve. Should have used the liquid, because I cannot follow directions.
I also found that if you use enough dye it will dye both sides.
I was not pleased with the results. My color was blotchy
After drying I went to place the cover on my phone and noticed that it had shrunk. I did not think that the cover would fit. It was short by 1-2mm on the side. But I centered it and pushed it down and it clicked into place. One benefit was that the creek from the battery door is gone.
As stated before the colors were blotchy. Also leaving it in there too long turned the cover black. Not what I wanted, but its better than gold.
I used a polishing wheel, like one that comes with a dremel, or knock off dremel.
This is my end result.