Kobuki, thanks for your reply and usefull information.
I do intent to write my own interpreter and this program will only run on one PC or Mac at the same time,
and that's the one I'm using at that time, so it's not a problem if it can't transmit to multiple computers.
The ESP8266 module I use is loaded with
this firmware.
I've used it succesfull with several other projects and it should be able to work for this project too.
I've attached the schematic and a picture of the PCB (without the AT45DB011 unfortunately).
Today I made another programming shield for this chip and used a CD4050 as a buffer between the 3V3 AT chip and the 5V Arduino ports, but still no succes in reading or writing the chip, so I'm not sure about what to try next. Any help on this is more than welcome.
Picture of the shield is also attached.