You need to ensure the SPI clock mode match properly between Arduino Nano and F28335. For example,
- If you select Mode 1 in Arduino Nano, you need to select options Rising edge, No delay in F28335
- If you select Mode 2 in Arduino Nano, you need to select options Falling edge, delay half cycle for F28335
to get the same SPI clock mode.
Ardunio boards - Mega 2560, Mega ADK, Uno, Nano 3.0, Micro and Leonardo uses 5V supply. Ensure that you use proper voltage level shift between Arduino and C2000 SPI pins for proper working of SPI.
Arduino boards - Due and MKR 1000 uses 3.3V supply. You can connect them directly to C2000 boards and get the SPI running.
Also ensure the Master and Slave is synchronized properly as discussed in https://e2e.ti.com/support/microcontrollers/c2000/f/171/t/545531?c2000-as-spi-slave-message-synchronization. You can make use of SPI receive interrupt in F28335 to read the data.