I have created a TFT screenshot viewer client that runs in the Processing IDE. It is called "Screenshot_client" and is in the Tools folder of a TFT library. This is a Processing sketch and it runs under Processing 3.3.
Processing is an image processing tool that has an Ardiono-like IDE. The Processing sketch can be changed to suit your own preferences.
Although the Processing sketch is within a library (targetted at the ESP8266) it is also applicable to other Arduino boards and libraries that are connected to colour displays, providing that library has a pixel colour read function.
An example sketch that contains the screenshot server functions in a separate tab can be found here: "TFT_Screen_Capture".
Each screenshot is saved automatically as sequentially numbered "png" images. Other image formats are supported (e.g. jpg,tif, bmp) by commenting/uncommenting lines in the processing sketch.
At the moment the Processing screen-capture client uses the serial port, another version that runs over a Wifi network connection is also in development, this promises much faster screen grabs for Arduino boards that have a network connection.
Have fun, report any bugs/suggestions here.
Example screenshots pulled off an ILI9341 based 240x320 pixel display: