Can I install flash memory?

Yes, both "CF to IDE" and "SD to IDE" converters will do. You will need the latest bios(2.20) though.
But be aware, that you can only change flashcards when the Z64 is powered off. Best buy would be an adapater with a 3,5" housing.
There are two kinds of these adapters, you need one where you can fit an IDE cable on to and not one that plugs into the IDE slot of an motherboard.

Adapter with a 3,5" housing bought from

An adapter from dealextreme with a custom build mounting plate:

Here you see a HDD and a CF converter installed at the same time: