Flatkvm is a tool to easily run flatpak apps isolated inside a VM, using QEMU/KVM.
flatkvm-paste can be used to send text to a Flatkvm session's clipboard.
flatkvm-paste accepts as a single argument the PID of a flatkvm process and reads the data to be pasted from stdin. This way, flatkvm-paste can be easily integrated into scripts and/or associated to keybindings on window managers like i3wm.
If you have flatkvm session running gedit, you can do something like this:
echo "Hello world!" | flatkvm-paste `pgrep -f "flatkvm run.*gedit"`
You can also use xclip (included on most distributions) to send the current clipboard contents:
xclip -o | flatkvm-paste `pgrep -f "flatkvm run.*gedit"`