I think you're correct in that the EMI occurs on the power supply lines, rather than in the chip itself. I've taken the usual steps---decoupling to the ground plane etc. I've also used a separate linear regulator for the SD card power.
When writing, the SD card seems to draw >50mA for microseconds at a time---it's difficult to tell exactly as the bandwidth of my current sensor isn't that high and the current pulses are (I hope) modified by the regulator and bypass capacitors.
I wonder if the noise relates directly to the current demands of the flash memory's charge pump that generates the programming voltage. When I get time, I'll take my RF sniffer (an old portable radio) and see if there's a significant difference in EMI between reads and writes.
Mark Borgerson