WindTerm
WindTerm is free and is available for Windows, macOS, and Linux.
Setup for Z88 Communication
New Session, then pick the Serial tab at the top. Pick your serial device (it will be a COM port for Windows users). Leave "Data" set to binary.
Choose Serial Protocol, then configure Baud Rate to 38400bps and Flow Control as RTS/CTS.
Sending Files to Z88
Now you can simply drag and drop a selection of files onto the WindTerm window to send them to the Z88.
Receiving Files from Z88
To minimise delays from handshake timeouts, the sending side should always be started before the receiving.