You can do it in Flashget itself. The Automatic option does, well, not exactly that, but what it does is, it allows you to browse the net, while downloading at a decreased download speed. It automatically adjusts the download speed so that the other programs which access net are given the priority.
You are looking for something like what disk defragmenters do, defragment while the HD is idle, but net can be used by any program like windows update, or even messengers, or antivirus updates etc. So, such an option, even if it exists in some download manager, will be very slow on downloads.
I suggest you try the automatic mode.