Hi,
I've had some personal experience with bad grains...they tend to oxidize once crushed. Putting them in a plastic bag does not help much since plastic bags are poor oxygen barriers. Heat accelerates the oxidization.
I would say a few weeks if stored in a cool dry place.
If you plan to store them for a longer time, put them in a proper oxygen barrier container (such as a foil bag), remove as much oxygen as possible and then put it in the freezer. This will let you store crushed grain for several months if necessary.
Cheers,
Brad