Yes, of course you can keep flour in the freezer.
For whole wheat flour, which is susceptible to rancidity due to the fat from the whole grain being included, it is even recommended.
For white flour, according to the University of Nebraska Extension in Lancaster County (emphasis added): For longer storage, keep white flours in the refrigerator in an airtight container.
All-purpose and bread flour will keep up to two years at 40 F in your refrigerator, according to the Wheat Foods Council.
They can be stored indefinitely in the freezer.
cooking.stackexchange.com/users/14401/SAJ14SAJ
Short answer, yes provided you emphasize the airtightness of your storage container.
I often trust the wisdom espoused on the forums of King Arthur Flour's website, and specifically this topic on freezing flour .
All commenters who report personal anecdotes with freezing flour report positive ones.
The one note that should be made is that self-rising flour could lose some effectiveness if frozen, "thawed", refrozen, etc due to the moisture changes.
Also note that if you remove the cold flour from the freezer and let it sit at room temperature it will gather moisture from the air because of its temperature (ala a cold glass of water gathering condensation.)
cooking.stackexchange.com/users/17833/Kaya
I've had great success freezing flour to kill the bugs.
It's important to keep the chilled flour in its sealed container as its brought back to room temp.
That way, condensation from ambient air will precipitate on the container and not the flour.
Same with baked products that you freeze to store--keep them sealed up as they transition to room temp, and a slight crisping in the oven will bring them to almost new.
cooking.stackexchange.com/users/71477/Lieto
I know this is a little late, but IMHO, you should never store any flour, pancake mix or corn meal in its original package.
That's the easiest way for bugs to get in.
Always store it in airtight containers (such as Tupperware or something like it).
Someone once recommended using glass mason jars with a good lid.
I always cut the date from the paper package and place that on the top of the flour (that I've stored in Tupperware)
so I can see at a glance when the best by date really is.
If you really don't use a lot of flour, freeze some and date it.
It will be fresh for months.
Hope this helps.
cooking.stackexchange.com/users/25535/Joey
I know it does when making ginger cookies.
The moisture picked up tends to make the cookies "flat" versus slightly raised with surface "cracking" which is so typical of ginger cookies.
The moisture completely eliminates the characteristic "cracking".
cooking.stackexchange.com/users/70945/David W. Herring
Whenever I buy bulk grains, flours, beans, I put them in the freezer for a month.
Or for years.
If the freezer ever dies then all that dry goods just starts a shelf life.
Freezing extends the life of these foods indefinitely.
And kills all bugs.
cooking.stackexchange.com/users/54047/SolarJimmy
I purchase Gluten-free organic flour mix from Costco.
It comes in a plastic air-tight bag with a tear-off resealable zip top.
I store it in the freezer and take only what I need and combine it immediately with all other ingredients.
Sometimes the use-by date has expired and the flour is still good, however, I am not a food scientist and cannot recommend using out-of-date anything to other people.
cooking.stackexchange.com/users/75499/Ella Fitzbag
Years ago I noticed I was getting little bugs in the flour that I kept in the pantry.  To prevent this, I started keeping my flour in the freezer.  I don't do a lot of baking, but I was wondering what effects this might have on anything I do bake.  Do baked goods turn out any differently when flour is kept in the freezer vs flour kept at room temperature?  Also, if it's okay to freeze flour, how long will it last this way?
Is it okay to keep flour in the freezer?
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<storage-method><freezing><flour>
cooking.stackexchange.com/questions/33890
cooking.stackexchange.com/users/18109/Fezter
Flour can be stored indefinitely in the freezer and its shelf life will be extended in the fridge. Freezing can kill bugs that are present, although repeated freezing and rethawing may affect the effectiveness of self-raising flour. Keep flour in an airtight container rather than its original packaging. You can keep flour in the fridge or freezer.
You can definitely keep flour in the freezer. It will kill bacteria and insects and extend its shelf life. You can keep flour in the fridge in a sealed container. You should never keep flour in its original package.