There is no need to manage downloading firmware updates to Saleae Logic products. As long as the latest Logic software is used, your Logic hardware will continue to run on the latest firmware.
Please just ensure you are running the latest release below.
The Logic software downloads the firmware to the device every time it is connected to the PC as shown in the image below. Before this point, the Logic device is acting as a simple bootloader.
If you are using the older Logic 1.x software, the following download link and firmware download image applies.