Is PowerShell installed on the server? You could do this in a CmdExec step type:

%windir%\System32\WindowsPowerShell\v1.0\powershell.exe -ExecutionPolicy ByPass -Command "& {$x=(Get-Date -Format "yyyyMMdd_HHmmss");Move-Item -Path "C:\@\FlatFile.txt" -Destination "C:\@\FlatFile_$x.txt"}"

Just change yyyyMMdd_HHmmss to match the timestamp format you want (see the options here) and the two paths to match your environment.