You might be surprised. I bought the same plates from the guy on the hide and at 500 yards my .308 would flip em right over. I had it mounted to a metal real estate sign and my chains were more vertical than yours.
The .223 will be fine but I bet that .338 flips it right over. I was shocked the first time I shot it.
If you are referring to those metal signs with two legs that they stab into the ground to hold their advertisement signs, then this frame is a lot sturdier than those frames.
This frame has angled legs to help absorb the force of the swinging and the chain will help dampen that. The chain between the legs will help make sure that the target legs dont extend any further and falls flat. So barring shooting the frame in half, I do not think it will flip over even with the 338. However, this Saturday will be a true test for the frame.
Or are you saying flipped around as in the sign flipped around a bar? I would like to see your real estate sign since most I have seen would probably just fall right over.