It seems to have varied a bit but this is what the official "Heeresmitteilungen" (Army Communiqués) has to say regarding the painting and treatment of canvas, the information is from a Missing Lynx forum post,
link :
H.M. AD 340-1937: Pattern painted tarpaulins have to remain with the earlier used (Bunfarbenanstrich);
H.M. AD 687-1938: tarpaulins actually painted in Bunfarbenanstrich pattern have to be repainted in dark gray / dark brown. Dark gray base paint must be leaving empty spaces for Dark Brown to be applied later.
H.M. AD 864-1940: as was lasts, all equipment and vehicles ordered to be painted in dark gray / dark brown are to be painted in dark gray only.
H.M. AD 281-1941: tarpaulins of vehicles to be used in Africa are to be painted in yellow and brown Graugrun applied for as dark gray / dark brown pattern.
H.M. AD 315-1942: Indicates H.M. 1128-1941 AD order (which I do not have) regarding pigments to be used thus for tarpaulins.
H.M. AD 181-1943: The Dark yellow and reddish brown base paints with Olivgrun camouflage paints are also suitable for tarpaulins.
H.M. AD 322-1943: Tarpaulins made from vegetal matter (hemp and linen) are to be left bare, treated but not painted over.
I've also tried to translate the german text of HV1945 no.52 mentioned in the thread with limited success:
H.V.1945, No.52:
Special regulations
8: Fabric and straps
a) Impregnated canvas of flax, hemp, etc. are still ongoing painting trials. For paper canvas green (RAL 6003) should be used.
Stocks may be used up. The application of camouflage to camouflaged wagon covers, etc. either has to be done with paints HE according to technical specification 6360B or camouflage paint after technical specification 6352.
b) For dust fabrics green (RAL 6003) or green and white (RAL 9002) should be used. The existing dark yellow cloth can be used up.
c) For all other fabrics the required color from the respective technical specification should be used.
d) Straps are according to use or order colored or natural colors (hue, according to to order) should be used.
Leather
Leather is used in it's natural-colored state.
The original german text of these documents can be found at: link