Well I was aware that the USB module is using DMA to transfer data SOC internally and independent from the driver.
e.g. p1288 in the K64F Reference Manual States:
"When a USB token on an enabled endpoint is received, USBFS uses its integrated DMA
controller to interrogate the BDT. USBFS reads the corresponding endpoint BD entry to
determine whether it owns the BD and corresponding buffer in system memory."
I had assumed that this interferes with with the channels used for SPI communication but didn't put the parts together. Turns out it is the initialization order of the modules. In my case I initialized the USBOTG module first and the eDMA and DSPI (Kintis SDK Driver based) module afterwards. This leads to conflicts because the USB module will make assumptions about the configuration of the DMA module which will no longer hold true after the initialization eDMA module and leads to interference in because it tries to use channels that are used by the DSPI module.
So the problem can be fixed by enabling and configuring the eDMA module before initializing the USBOTG module. In this way the USBOTG module recognizes that the eDMA controller is used for other purposes as well and doesn't cause interference
Thank you very much for your input - you definitely pointed me in the right direction!