I don't have that screen so I cannot test it, but I'd recommend you to check if there is data from the Edison SPI. I saw that there is a library provided by Adafruit, however it is for Arduino. Sometimes the Arduino libraries don't work on Edison because there are architecture differences. The libraries might end in errors during compilation, or they can compile but they simply don't work on Edison. In a case like this, you would have to write your own library to be Edison compatible, however, it isn't an easy task.
I gave that a shot starting with stuff at https://github.com/intel-iot-devkit/upm/tree/master/src/st7735 upm/src/st7735 at master · intel-iot-devkit/upm · GitHub but no luck.
I can get one of two things to happen:
1. If I connect everything via 3v3 then I just get a white screen
2. If I connect LCD to 5v but the rest to 3v3, then I get a randomly garbled screen UNTIL I run the upm code. Then it goes white until I power cycle.
In no cases do I get activity on the screen as far as images getting displayed.