I don't know Flutter functionality, but it's always possible to do the following trick.
You must have access to the Windows file system and administrator rights in order to pass a command to executable exe files that are the starter file to run the code of programming languages designed to execute Windows commands.
C:\Windows\System32\WindowsPowerShell\v1.0\powershell.exe
C:\Windows\System32\cmd.exe
C:\Windows\System32\wscript.exe
C:\Windows\System32\vbscript.exe
Maybe the following link will be helpful for you to take the first step.
How to run a PowerShell script without displaying a window?
Maybe it's even a second step, but you'll still have to go through it if you don't want to have Windows executable flashing windows while your program is running or maybe vbscript.exe otherwise.