SD cards are so nifty. I see them as little tiny floppy disks except that they have gigabytes on them. The micro sd cards are so tiny you sneeze and they can disappear.
So -there are some huge advantages to getting them working as an add-on for old computers.
The problem is the interface. There are not many examples of working code out there, and if you do have working code, it isn't quite what you need. At the bitbang level, sd card code is complicated.
There are three other approaches that might be worth pursuing. One could be to join Andrew Lynch's group (N8VEM) and then you will have access to all the files and in one of those files are the five Z80 assembly programs I wrote to talk to the uDrive
http://www.4dsystems.com.au/prod.php?id=22 $29
This enables you to read and write files to and from the sd card via a serial port (tested to 38k baud, but ought to work up to 115k). It would just need some tweaking in the source code to change the port locations.
Another option is to look at other CP/M boards that have SD card access. I'm working on a propeller emulation
http://www.smarthome.viviti.com/propeller and this board uses an sd card with eight 8mb disk drive images that use the Altair SIMH format. This board also has xmodem, and it is easy to xmodem files back and forth between other CP/M boards, either with wires or wireless. So this could be a solution if you have xmodem on the Kaypro, as then you don't need to do any coding.
Though if you have xmodem on the kaypro, you can also transfer files directly froma PC. And if it is tedious sending them one at a time, you can set up batch file transfer (code also at the N8VEM group).
As for reading the sd card directly with Z80 code, as far as I know only Juha at the N8VEM group has managed to do that, but he has disappeared and while his code is still there, I'm not sure anyone quite understands it. You would need 4 generic I/O lines (eg from an 8255) at 3V logic levels and i'm not sure if that would be all that easy to do. RS232 would be a lot easier.