Example how to run program and write stdout and stderr to file with timestamp:
cmd /c ""C:\Program Files (x86)\program.exe" -param fooo >> "c:\dir space\Log_%date:~10,4%%date:~4,2%%date:~7,2%_%time:~0,2%%time:~3,2%%time:~6,2%.txt" 2>&1"
Key part is to double quote whole part behind cmd /c
and inside it use double quotes as usual. Also note that date is locale dependent, this example works using US locale.