Is it possible to download music to my Sony Walkman Video MP3 Player using my RCA Galileo Pro 11?

If this Sony needs proprietary software to transfer music, no. If it is seen as an ordinary USB drive when connected to a PC - a simple $5 USB OTG cable (so that the Sony will be seen as USB drive for the tablet) is all you need, plus a file-transfer utility on the tablet to copy files across (assuming you have them already downloaded on the tablet)
Do you mean transfer music from the android tablet directly to the mp3 player?
If you could find the right kind of USB cable you could try it. Have no idea if the phone would see the mp3 player as a usb drive.
I think you would have to transfer them to a computer first.