How can I make my ILI9486 Display not show my frame until I'm done? (Flickering!)
Most graphics libraries use a frame buffer, and copy this to the LCD in one go. Preferably with DMA.

This frame buffer keeps one full frame in memory. The advantage is quick rendering, and glitch free updates. The drawback is a large memory footprint.

The ILI9486L only has one frame memory, and you can only directly read/write on this memory. The LCD is continously refreshed from this same memory.
The controller does offer features to reduce tearing effects, but it does this by advertising on which row the controller is currently refreshing. 

If you update to an LPC1788 you have the option to use an external memory to keep a frame buffer. 



A workaround could be to use a smaller section of the screen as buffer, draw in this buffer, and then update this buffer quickly with the DMA.
You might also be able to limit the effects by increasing the speed of the communication.
And of course, you can use smarter drawing algorithms so that clearing the full screen is not required. You can also read from the LCD.