The most likely cause of this problem is that the flash drive may require a driver which you do not have installed on teh windows 7 machine. It is even possible that the flash drive maker does not have a windows 7 version of the driver available.
I would recommend going to the manufacturers web site and looking to see if they have a driver available for download for windows 7 or an earlier version.
Another potential problem is that the USB ports on the windows 7 box are either not enabled or are not the correct USB version.
You may wish to open device manager in windows 7 prior to plugging in the device, then plug the device in and observe if it is recognized in any way in device manager - typically the machine will emit some sound and you will see a change in the devices list shortly after plugging in a USB device. If you don't observe any change, then the port is either disabled or does not recognize the device.
A good thing to try at that point is to plug the device into another machine running anything other than windows 8 - if it works there, then the problem lies in the specific windows 7 machine.
Lastly, and this one will sound like it wouldn't have any impact - but it can... Plug the device into a USB extension cord first, then plug that into the computer. I don't know why this has an effect, but I have seen it work on too many occasions to question it further.