Really great question Joshua!
My thoughts are to not grow on just flour, but some mixture of flour and
straw, flour and
wood chips, maybe flour lining the inside of a log.
If you are wanting to do this inside I might consider getting a 5 gallon
bucket full of straw and thoroughly wet it down and pack it in just as you would for any other indoor mushroom
project. But maybe after getting it all wet, sprinkle in the expired flour so that it sticks to the straw. At that point you can spread in the spawn and maybe just a little more flour to top things off. Hopefully the flour will act as an accelerant for the already fast decomposing straw and get you your mushrooms that much faster.
I think this is worth some experimenting, so please let us know how things work out.
Eric