Flour is a raw agricultural product and can thus be affected by pests, including tiny beetles which can easily go inside the bag. This possibility alone may convince you to store your flour in the fridge, but there is another reason to do so.

Flour can and will go rancid since the oils in it degrade over time, so when you bring a fresh bag home from the grocery store, carefully decant it into another container with an airtight lid. The refrigerator is more humid than the pantry, and too much moisture can make flour moldy, so when storing it in the fridge, it's important to do it right.

You can find containers to store flour online or in most kitchen supply stores, but make sure the seal is airtight. Once your flour is in the container, you should add a label and mark the date you bought it and the best-by date on the original bag.