Does anyone know where I can get an MP3 instrumental version of the Brady Bunch theme song?

Here is a karaoke version (without any lyrics), it might be the best you can do - http://www.sitcomsonline.com/sounds/thebradybunch-karaoke.mp3

Hey not bad at all..... Did you do that TJ??

An instrumental version in chamber music style appears on the CD "Mozart TV" by the Hollywood Chamber Orchestra.

You can listen to a preview of it and buy it here:
https://www.amazon.com/Mozart-T-V-TV/dp/B000000715

You can always use my go-to source for instrumental versions of many songs. Hit YouTube and search for "brady bunch karaoke." There's not only the theme, but things like "Keep On," "Time to Change" and "It's a Sunshine Day."