On UNO also it shows unrealistic colors and same flickering kind problem appears.
If you have got the correct ID, the TFT will behave exactly the same on Uno or Nano.
Neither Uno nor Nano are permitted to supply large currents from the 3.3V pin.
Seriously. Develop on proven hardware e.g. Uno + Shield.
When debugged, you can transfer finished project to the soldered Nano.
David.