I've been doing some research on what you can and cannot dry pack (with an oxygen absorber packet).
For long term storage, products must have a low oil content and have 10% or less moisture content. Otherwise you risk rancidity and botulism poisoning.
So, DO NOT dry pack the following items:
Whole Wheat Flour (*Wheat berries are okay*)
Milled Grains (*Rolled oats are okay*)