What's the best way to store flour?!
Any flour will keep in the freezer longer than at room temp or even in a "cool" place, since the bugs in it won't hatch unless the temp gets warmer.
Whole wheat flour also has oil in the germ part of the grain and it can become rancid after some period in storage.
Most people don't have room in the freezer for flour though, or consume it quickly enough not to be a problem. In that case, it is best to keep it in a place bugs can't get into.
(I keep all my flours in the garage freezer, in ziptop bags. Then I never have to worry about them. Usually I just use them as is, but a few recipes are better if the flour isn't too cold...some are better if it is cold.)
Sugar will last almost forever just at room temperature. It's a natural preservative all by itself. It can begin to clump if humidity gets too high and it's not air-tight, but just stirring will fix that.
More info on storing flour (short term and long term) here:
If it's been opened, you can keep the flour in it's packaging, but you should put it in an air tight container and store it in a dry place. You can also remove the flour from the packaging and just do the rest of the steps without it. Yes, flour will stay just as fresh if it is stored in the freezer. Despite of what someone above me said, flour does not stay fresh unless it is properly stored. Brown sugar will also stay fresh in an air tight container, there hasn't really been much prove of it staying fresher in the freezer though.
I use a small one of these for granulated sugar and the large for flour. They keep well and look great on the counter.
It's best in the paper bag that it comes in. It's packaged that way for a reason. As long as you store it in a cool dry place it will stay fine for years. The same goes for sugar. x
I would just use an airtight container left at room temperature (too cold it can harden)