How much current does the back light of ILI9341 LCD take?
You are asking a trick question.
The assembled LCD module consists of a display module assembly with a suitable backlight assembly.
The fact that it has a ILI9341 TFT controller has very little to do with the backlight, even though the brightness may be controlled via ILI9341.
The answer to the backlight specs would be in the datasheet of the whole LCD module, not in ILI9341 TFT controller datasheet.
So you must know the part number for the whole module to find the datasheet for it.