One of the tough things about Disney history is determining the abilities of the directors. Walt Disney was always the final arbiter of anything that went on the screen. How much of what we see in the Disney shorts of the 1930's is the work of the directors and how much is Walt Disney or the crew?
In Burt Gillett's case, we have a pretty good idea. At Disney, Gillett directed some fairly notable cartoons: Flowers and Trees, The Three Little Pigs, Mickey's Gala Premier, Playful Pluto, Lonesome Ghosts and The Brave Little Tailor. Walt Disney obviously had faith in him or he wouldn't have assigned him such important cartoons.
Other studios were interested in Gillett because The Three Little Pigs was one of the most successful short cartoons ever made. The Van Beuren studio hired Gillett to upgrade their films. While today we have a fascination with the quirkiness of the Van Beuren cartoons from the early '30's, at the time the studio was stuck with a silent cartoon drawing style and unable to create popular characters.
Gillett converted the studio to color production, upgraded the drawing and bought rights to characters like Felix the Cat and Toonerville Folks. The studio created original characters like Molly Moo Cow. If you've seen these cartoons, they're far slicker than Van Beuren's earlier films but they still lack strong stories and characters. When Disney made a deal to distribute through RKO, RKO dropped the Van Beuren cartoons and the studio closed.
Gillett returned to Disney for a couple of years but left again in 1938 when he moved to the Walter Lantz studio. He worked on the first few Andy Panda cartoons and a couple of fairy tale spoofs, but his cartoons at Lantz resemble his Van Beuren work far more than they do his work at Disney.
While Gillett was present at the birth of personality animation at Disney, I don't think that he really understood it. The ghosts in Lonesome Ghosts are interchangeable in a way that the three pigs are not. The giant in The Brave Little Tailor is thinly conceived; he's not as interesting as the big bad wolf. With the possible exception of Andy Panda, Gillett wasn't involved with a successful character outside Disney, and Andy was stolen from Fannie Brice's radio character Baby Snooks.
In his biography The Walter Lantz Story, Joe Adamson quotes Lantz saying, "Burt had to do things over and over and over again. He was a trial-and-error person....Gillett never knew where he was going." It took Disney and his story department to give Gillett something to run with. Away from Disney, he couldn't manage it himself.
Gillett left the animation business in 1940 but lived until 1971, dying at the age of 80. I have no idea what he did after leaving animation, but I'd be curious to find out.