I have zero experience with dying hypalon, which is what this gear is made from.  Standard procedure for dyeing nylon is to use water just off the boil.  I have no idea whether or not such temp will harm hypalon, or be OK.  If you are able to obtain some sample bits of hypalon in grey, then using such on tests would be a very wise idea.  I once destroyed a Bundeswehr plastic mag pouch using temps that would be OK with nylon fabric.

In my experience, the tactical colors that have worked best on nylon fabric are Rit Taupe (brown), Apple Green (light green), and Dark Green.  As stated, I've never started from a gray base before, and the general rule of thumb is that it is possible to dye darker, but never lighter.  If, in fact, the hypalon is capable of accepting rit dye, then I reckon it should not be too hard to achieve some sort of mediun or dark green or brown.  I advise against going too dark.  I'd communicate with the mfrs/vendors of such gear, and ask to buy samples of grey hypalon.  With any luck, they will give them to you, or sell them cheap. 

In any event, if the belt and/or chest rig is fully covered with pouches/panels of the desired hue/camo pattern, then the grey color of the base belt/chest rig becomes almost irrelevant.  Not that I would advocate filling them all, mind you, just the bare essentials.

Some folks will no doubt suggest dusting the gray hypalon material with paint.  In this case (and not having done it myself), I would suggest using alcohol to remove any surface contaminants/release agents before dusting.  I'd also try to use paints that were advertised as being made so as to be particularly applicable to plastic; IOW, increased adhesion.  If you can prep the hypalon with alcohol, and use the right paint, then you have a decent base color to work around.  It might be possible to obtain a respectable camo pattern, even with dusting.  Perhaps some sort of ATACS camo pattern.  The problem with dusting with paint is first, getting the hang of it; there is a technique.  The main point is the adhesion of the paint--it tends to wear off.  OTOH, I've not heard from people who cleaned the to-be-painted surface with alcohol, nor have I heard much from people using paint that was designed to be used on plastics.  Again, no expert, but such steps are simple common sense.

Flexithane Paint is intended for use on Hypalon material.  Unfortunately, not yet available in tactical colors, but at least we now know that there is paint suitable for such material.

After further googling, it appears that there is a wide variety of custom-mixed hypalon-suitable paints available.  So, that might be the way to go.  I have zero info on how durable such paints might be.

Search using search term "painting hypalon".