Better 3D graphics on the Arduino: avoiding flickering and tearing

A while ago I purchased a cheap TFT LCD Arduino shield from Ebay (e.g 1 2 3). The board arrived with no documentation. Disassembling the shield revealed no ICs, indicating that the driver is integrated with the LCD itself. Upon request, the vendor provided an archive containing a few amusingly translated datasheets, as well as a copy of Adafruit's Arduino LCD drivers. Evidently the product is a clone of the Adafruit LCD shields, and uses the ILI9341 LCD driver. I had hoped to use the display to show short animated GIF loops. This is not, in practice, possible. Test animations loaded slowly, with noticeable flicker and vertical tearing. The Arduino does not have enough speed or bandwidth to render full-screen animation frames, but what about 3D vector graphics?