If I am not mistaken, the double and triple box is the ancestor to the flare box. What the barge box had over the flare box in the early years, was you could take sides down/off and convert it to a flatbed/hayrack. Also, the barge box was larger in capacity than the double/triple box which was a bonus. I believe the galvanized flare boxes were created years after barge wagons had established themselves after the old double/triple boxes.
The larger/longer barge boxes, 14ft+, had sides of 18" where the 10'-12' boxes had sides of 28" +/-. I have two 7'x14' barge boxes with 19" sides.
When I was growing up, Dad had both a barge box and a flare box. The barge box was larger, and so would hold more corn, especially with the extra sideboards we had on it.
As the one who unloaded the wagons, I liked the flare box better for unloading. Reason was the tailgate was the full width of the box, so the corn ran right out. The tailgate on the barge box was narrower, so the corn would hang up in the corners, creating more work to get it all out.
All I can find around me here in Central Missouri are barge the longer barge boxes with 18-24 inch sides. I would like to find a flare box but nothing is close to home. My thought is most everybody in this area square baled hay so they could take the sides off the barge box in the summer and put on a hay rack in the back and haul hay. That way they had a dual purpose wagon
Dad, stubborn old Swede that he was, kept using flare box wagons as long as he farmed. Barge box wagons, you had to dig and rake the corn out of the back corners, waste of time and effort he said. Gravity box wagon could have dumped into our inside elevator at the home farm, and probably laid over on it's side on some of the hills we farmed! Was fall of '66 Dad bought the Oliver (EWC) #5150, 150 bushel flare box and mounted it on a Oliver(EWC)) 5026 8-ton gear. I forget the brand of hoist, twin cylinders that straddled the center reach, was low enough the box sat down tight on the frt and rear bolsters, could run two feet of sideboards easily, and the wagon was wide enough no bang boards required. So you could haul as much as a barge box, no corners to clean out, and equal load at all four corners. But when you got that wagon full you had to watch where you drove hauling in, we normally hauled in with a Super H. If it was a little wet it struggled.
Over at the 80 We farmed with the neighbor we unloaded into the elevators with the picker tractors, wagon hoists plumbed right into the picker hydraulics. Short Half mile rows, 2 rounds most years and the wagon was full, on the full length half mile rows you might take one row on one pass. Back of the farm was a meandering creek.
We had a separate hay rack, 16 ft long, 7 or 8 ft wide on about a 4 ton gear. We used the flare box wagons without sideboards to combine oats, unloading on the go with our pull type combine. The unloading auger on the Deere #25 & #30 combines wasn't long enough to reach over any higher sides.