Box flexing shouldnt be an eye noticing thing. Its an ear noticing thing.
If you see (with your own eyes a box flexing) then you have a real stupid problem for sure.
Bracing is used to stiffen the enclosure(or better yet, reduce hollow sound, AKA boxy sound from your enclosure).
One good way to test a box to see if you have a decent enclosure is to knock on it with your knuckles. A poor enclosure would have a low pitched long duration hollow sound, where a good enclosure would have a higher pitched shorter sound. I would say that if box sounds as if you knocked on your kitchen table as compared to the sound you would get from knocking on a 3" thick piece of brazillian cherry hardwood floor plank, then you have a poor designed box.
BTW I doubt that there is such a thing as 3" thick brazillian cherry hardwood planks, but I am just trying to stress out the difference in sound.
Or just knock on the edges of the box, and then knock in the middle of one of the sides. If the sound is much different, then you have a poor built box. Poor as in, it will sound boxy.
Basically you want to hear only the speaker, and definetly nothing else. No rattling, vibrating, port noise, no boom (AKA overhang), nothing ...
Its an ear noticing thing. 