By default, the Pi 3B will not boot from flash drives.
Create a working SD card with Raspbian Buster Lite first then boot from this SD card first. When you are at the command prompt run
echo program_usb_boot_mode=1 | sudo tee -a /boot/config.txt
Once the reboot is complete, run
vcgencmd otp_dump | grep 17:
You should get ** 17:3020000a**. If not try again and if it still fails you may have a duff pi.
The above has told the firmware that it can boot from USB as well as SD card.
Once this is complete, make sure your download is correct by checking the SHA value of your file vs the web site and use Etcher with verify mode ON to write the image to the flash drive.
Though I’ve not used retropie, it looks like you can add the programs to a working image based on this KB so I would build a Buster (assuming Buster is supported) onto the stick first, get that running and then add the software to this.
One other though is to boot from SD then mount the USB and use that to store the ROM images. Many YouTube videos on doing this.
I have found the Pi very susceptible to USB insertions / removals - I think it’s a ground loop issue but not tracked it down yet!