The Stipula T-Flex is the only titanium nib I know of that is expressly billed as "flex", though no where near that of a gold Pilot FA (falcon) nib (not to be confused with the "S" [soft] nibs of the Pilot Falcon pens). It has just a touch more "flex" than the Bock titanium nib on a Ranga. Other than the Ranga/Bock, my titanium nibs are on Stipula (or Levenger from when I'm sure they were commissioning models from Stipula -- back then Stipula was the only company I knew of that used titanium).
The Pilot Custom 912 with FA nib is the first pen I've encountered that I would consider "flex" (in my mind, the Noodler's steel "flex" nibs, Conklin/MonteVerde Omniflex steel, Pineider "Quill cut" "Hyperflex" gold are barely flex*)
As for "feel". I currently have one titanium inked -- the Ranga, along with a Ranga with a Bock gold nib. The titanium as a subtle "pencil" feel -- and scritchy sound. I need to finish the ink load and try a different ink, as the Diamine HoneyBurst is too pale for my taste, and I might be trying to compensate with added pressure.
Note that gold does NOT EQUATE to flex. The aforesaid Ranga/Bock gold nib is very smooth, and quiet, but shows no variation with the amount of pressure I was comfortable trying.
$200 budget -- not going to find many gold nibs these days, and they likely won't show any flex. You just missed the last Ranga group buy with Bock titanium nibs (and feed units -- you could try one and later purchase a Bock gold nib for comparison... Note that where a titanium nib added about $50 to the base price of a Ranga, the gold nib alone adds $175 or so). Platinum has a few models with gold nibs at under $100, but don't try to flex them (Japanese EF and M as I recall). The next step up would be their "Modern Maki-e" series, around $150.
*Caveat: My main criteria is NOT how wide the tines will spread, but how much pressure is needed to produce variation -- if it takes muscles to flex at all, it is not a "flex" nib to me. A Conklin DuraFlex gave 0.4x0.2mm expanding up to 1.0x0.6mm; a Stipula Model T gave 0.4x0.4mm up to 1.0x0.4mm -- so about 2.5X variation.