This will be easier than two 25 lb. 6' boxes, but, yeah, I understand where you're coming from.
The most difficult aspect of lugging around a bag of flour that size is that there's nothing to grab, so, unless you have the bag balanced over a shoulder, you really need two hands for it. Just off the top of my head, I'm thinking duct tape might help. Maybe you could fashion some sort of handle. If you really wanted to go crazy and had enough tape, you might be able to fashion a back pack out of it. If you do use duct tape, make sure you go all the way around the bag with it and do a few layers for strength. If your makeshift handle breaks at the wrong moment- that would be bad
It might be more carry-able if you make the handle on the side rather than the top. That way you can carry it like a bag. Here, take a look at this:http://used-handbags-for-sale.com/wp-content/uploads/2009/01/prada-handbag.jpg
Do you see how the straps go all the way around? That's probably what I'd do with the duct tape. Don't forget that duct tape is weak laterally, so make the straps pretty close to the center. Hmmm... maybe you could run the duct tape around a short piece of broom stick and use that as the handle. The broomstick would be comfortable to hold and you could loop the duct tape straight so it doesn't twist or bend. In fact, you probably just put the broomstick against the side of the bag and tape around it nice and tight. As you pull on the stick it will naturally give you enough space for your hand. Can you picture this?
Do you know anyone with one of those folding shopping carts? I see those all the time in the city. Something like this would be ideal:https://www.amazon.com/dp/B0000UZ57S/?tag=pmak-20