May be something simple like bit-banging the SD from the parallel port with a level shifter to 3.3V. Not going to be fast as you are limited by the E clock cycles (< 200kB/s), but doable. You can probably whip up a device driver that make it look like a block level device.
Oops. Wrong units. bits.
"Arduino" SD breakout boards from China/Ebay that has on board level shifter already. Matter of hooking up the pins to the parallel port.
If you can move a hard drive from the Amiga to the PC, then there are ways of reading that off. For linux, it is easy. For windows, you can copy files on the hard drive/hard drive image file with this: