I don't think I've ever seen a (mostly stock) Triumph whose frame didn't flex or sag a little bit. It's part of the design, I assume.
It's hard to determine what degree of sag is acceptable. Sag of more than 1/2 inch or so (which would seriously pinch the doors shut) may be excessive and warrant professional diagnosis. Having said that, however, I've seen plenty of Triumphs with that degree of sag run for thousands of miles with no problem. I don't think I'd want to race/autocross/thrash a car like that, tho'. If unacceptable sag is found, the frame may be repaired. This should be attempted only by experts, though.
You can also carefully inspect the frame for rust/weakness by going over every inch of the frame with lots of lighting, tapping vigorously with a hammer, and a very close visual inspection. This isn't an exact science, but it may uncover serious defects in the frame.
Frame damage is something to look out for when buying an LBC. I got burned once on a GT6 with a bent (front) frame, it cost $1600 to pull it straight. Closer inspection would have detected it, but the car was otherwise very nice and it passed an alignment test, etc. The giveaway was the front suspension was shimmed all the way out to the right to compensate for about 1 1/2" of a bent frame. I shoulda seen it, but was too busy drooling over the car. The "professional" alignment folks didn't catch it, either. Finally, a Triumph guru (Joe Hash of Joe Hash Triumph, Ltd. near here) showed it to me.
Buyer beware: a close inspection can often uncover frame damage/rot. But sometimes not.
