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Thanks for reaching out!
I believe the issue may be due to the code that you are using to control the screen. I mean, the SPI bus on Edison can handle a maximum frequency of 25 MHz according to the Module's Hardware Guide (http://download.intel.com/support/edison/sb/edisonmodule_hg_331189004.pdf) and the screen driver used on the shield that you shared (http://www.waveshare.com/w/upload/0/09/HX8347-D_DS_T_preliminary_v01_081129.pdf) has a maximum oscillator frequency of 2.94 MHz.
Since I don't have access to this screen this is just a guess, but I don't think that the issue is related to the SPI bus but instead on how it's being used. If you use mraa (https://github.com/intel-iot-devkit/mraa), you can easily change the SPI frequency. You can learn how mraa's SPI API works in https://iotdk.intel.com/docs/master/mraa/spi_8h.html#ac0c9c78a52d6c1f9733eba821ec9dcc8. In the following example: https://github.com/intel-iot-devkit/mraa/blob/master/examples/spi_max7219.c, you can see how to set up the SPI bus including the bus’s frequency.
My suggestion is that if you are not using mraa, then try interacting with the screen using this library. I believe it will be easier this way. If you have issues doing so, read the datasheet of the screen and the touch sensor driver. They will provide you a lot of useful information that will clear most of your doubts. They can be found on the link that you shared (http://www.waveshare.com/wiki/2.8inch_TFT_Touch_Shield).
I hope this information helps you,