This phrase is unique to the alternate universe wherein Ben, Thomas, and Bob were born.
“Flak” is what military planes take when they’re under fire.
The “pack” is the last vehicle in the military formation. It’s carrying all the supplies your force needs– food, tents, ammunition, replacement parts. You put the supply wagon at the back of your force because it’s slow and because usually the danger is in front.
If the last plane in your formation is carrying all your supplies, and it gets targeted with anti-aircraft fire, it’s taken flak.
So, to “flak the pack” means to destroy everything you needed. If you did it to yourself, you were supremely stupid.