would increased wing flex be looked at as part of the certification process? Is wing flex even increased, or is it just more apparent from the cabin on the wingletted models?
Definitely... and from many different points of view.
First, the primary reason for adding the winglets, overall drag reduction, has to be evaluated by aero, and the results incorporated into the performance models. The aero guys will want to account for wing flexibility in their models, and there would probably be wind tunnel testing as well. Aircraft handling and stability also has to be re-evaluated.
The loads models would then need to be updated, not only to account for added weight at the wingtip, but also to account for the changed loads distribution on the rest of the wing... you may end up actually increasing your wing root bending moment for design maneuvers.
And that's just the "static" loads. Even more importantly, the dynamic effect of the winglet has to be analyzed. Changing the mass of the wing in that way, and the aerodynamics of the wingtip as well for that matter, will have an impact on flutter. The added mass will change the fundamental structural modes of the wing. Probably, you will have to do a partial ground vibration test with the added winglet to tune your flutter model. Once you have a tuned structural model, you have to evaluate your "dynamic" loads, such as landings and gusts, as these have a tendancy to shake the wingtip around, and the results of the analysis depend on knowing well the structural modes of the aircraft.
Of course changes to loads mean stress analysis. The objective would be to make sure that with any loads changes, you're not reducing your safety margins to the point where you have to introduce structural changes to the wing. If your wing is built by a partner or a supplier, you definitely don't want to worry about design changes, because then contract considerations come into play.
More than you probably wanted to know about the subject, but adding a winglet is far from a simple undertaking.