is the clock supposed to be varying widths when the Arduino acts as a SPI Master?
I would not expect so because it's hardware driven and should be stable, there may be a gap between bytes though.
OTOH there's no reason not to vary the clock with SPI.
What are the sample and target clock speeds? If you aren't sampling fast enough relative to the sampled data you will get an effect that looks like the clock varies. This is were the external clock that Retroplayer mentioned can be handy.
Rob