Ah... you may have a problem. Dyes need a high temperature which will probably seperate the flexible plastic coating from the back of the material if it is coated. Some synthetics wont take dye at all.
The best method would be a pack of blue or black washing powder based dye made by dylon, you can get it at tescos. The little tins are dead tricky and not reccomended.
Method
1 Scrub sack with nail brush for encrusted crud, not forgeting to remove frame and as many metal bits as possible. Padded straps can be a problem as the foam will be full of dye
2 Wash sack in machine to get it clean and wet, this enables the dye to get into the fibres.
3 Throw in the dye pack and do a high temperature wash.
4 CAUTION THE DYE POWDER GETS EVERY WHERE WEAR GLOVES!
5 Immediatly after washing hang out to dry- then remove gloves.
6 Run an entire bottle of bleach through the maching to remove residual dye.
7 Mop down door of machine and surrounding area with a mild bleach solution.
The blue should give you a green tone and the black probably a green/brown in the yellow areas. The blue will do the same but deeper tones. Who knows it may actually dye it deep enough to hide the lot.
When dry apply a couple of coats of silicone based water proofing and thats it.
Most military clothing will take this method and it will last a long time.
All this is based on my exwifes desire to change the colour of everything... madness!
The dye is cast
Sandsnakes