In the FAQ it is stated that PKHeX doesn't work in Linux. With the latest wine (8.12 at date of writing) however, it is possible to run PKHeX in Linux.
Instructions:
Make sure you run the latest version of wine. Download it here.
Install winetricks according the instructions according to your distribution. Update it with sudo winetricks --self-update
Install dot.net 7 and dot.net desktop 7 with winetricks -q dotnet70 dotnetdesktop7
You can now run PKHeX in Linux.