frame flex with anti sway bar

not sure what frame flex is.
but they are mounted to the frame behind the rear axle, as well as mounted to the rear in 2 places. As the truck body tries to role (the springs allow it to role) the sway bar will transfer this role effort to the opposite side of the truck frame

Yes, it can add frame twist just by the fact that it tries to eliminate axle articulation. Your truck however should not have any frame flex since its a boxed frame and designed to be rigid.

https://www.youtube.com/watch?v=_f3CAnH7WIM

It is favorite competition sample, that Fords, when lifting rear wheel off the ground often are developing tailgate bulge due to frame flex.
There is flex to everything. Golden Gate bridge flex under full load several feet.
Coming to anti-sway bar, they transfer relatively small power, just like weight distribution bars, or even less. If you have to worry about flex due to bars, than you have bigger things to worry about.
Lately I noticed that anti sway bar on wife Mercedes is thicker than the one on my F350 dually..

hmm.....

Sorry, I was just posting that as an example of frame flex or frame twist. I definitely don't want to turn this into another truck bashing thread. I like the Ford a lot, especially the motor and trans.

If the frame does not flex at all, the ride will be harsh! it also increases the chance of cracked frame. It is made to flex to some degree.

Yes, it will twist. No, it's not bad for it.

Dump trailer with a very full load of sand. This is with a big wig sway bar installed.

You are not showing close up, but looks like the gap between tailgate and right side is bigger at the top, than at the bottom. That is sign of flex.
Other is comparing space between top of the bed and cabin on both sides.
Wait a minute, isn't the space the bed and rear glass a wedge?

I am not sure what wedge your referring too? The tailgate had no issues, as I had to let my dog Cooper out.

That was a fun day. Six very full loads of sand for the dry lot.