A sampling of what little was completed is available online. Watch the six-legged Thoat's run.
The project, sadly, fell through when Clampett and Warner Bros. couldn't see eye-to-eye on the tone of the project, which Clampett wanted to be big and epic and pretty serious, and which Warners wanted to be comedic, almost wacky.
It's an amazing what-if for animation fans: what if (ideally) two animated masterpieces had materialized from two different sources in short order? Just the fact of these two different approaches to telling stories via animation -- Disney with his fairy tales and fables, Clampett with his sword-wielding otherworldliness -- may have prevented American audiences from getting so used to the Disney formulas of storytelling, where many things are cute and family-friendly. (Yes, I and Brad Bird remain annoyed that many people consider animation a genre instead of a medium, able to tell all sorts of stories. Animation should be less ghettoized!) Conversely, would Warners' Looney Tunes have become the pop-cultural force they became if the studio had been making animated features? Much could've been different -- a different history of classics, good work, not-so-good work, and utter crap. History tends to work like that, even alternate history. Not all animation would've been brilliant, but not all animation is brilliant. But still: imagine. (I'm sure happyspector would have an especially good time imagining...)
The John Carter of Mars stories are too good and cinematic for filmmakers to resist adapting, and finally Pixar is making a go of it -- after recent attempts by Kerry Conran, Robert Rodriguez and Jon Favreau have fallen through -- with what Pixar hopes to be a trilogy. Just in time for the 100th anniversary of A Princess of Mars first appearing in print!
(Animation link pointed out by zarq) (Edit! Actually not by zarq -- I was thinking of something else from him -- but by Ain't It Cool News)