AFAIK, Flexon is not just titanium.  It is instead, something akin to NiTinAl shape-memory alloy.
Have a looksie at:
http://en.wikipedia.org/wiki/Shape_memory_alloy
especially, the section on pseudo-elasticity.  Neat stuff.
I've been wearing flexon glasses since before the trade name flexon existed, and was originally told about a proprietary heat and mechanical process for creating that special alloy.  I suspect that GTAW might be able to fuse the frames, and that NiTinAl might even be a suitable filler, BUT that the localized heat would leave a large section in an unsuitable metallurgical state.

Many glasses are made of titanium, and would probably weld better with CP titanium filler.

In any case, every pair of metal frames I've seen, are completely covered in a lacquer of sorts, and usually is plated first.  EVEN if the end finish appears to be shiny metal.
The plating probably makes polishing and finishing easier, and the lacquer is important for corrosion protection.  Even the titanium frames I'm wearing right now, which have a "titanium" finish, have a clear coating.
I've got a pair of flexon frames (which were bright silver), where on the inside, you can see layers, where the clear finish wore through, and then, where what appears to be bright nickel plating wore through to expose another duller alloy underneath.

I'm sure that any finish would be completely ruined by GTAW, and would make the glasses seriously ugly, and that AND any plating should prevent any fusion welding.

On another note:
I've been wearing this type of frame for a LONG time, and have broken MANY of them.  Yeah, its more durable than nickel-silver, and even stainless frames, but nothing lasts forever.  The best advice I can give, is to foster a good relationship with your optician.  No matter how elastic an alloy you use for glasses, they eventually work harden, and snap, and its nice to get replacement parts, at, or near, cost.