Quoted from the (excellent) Bellagio 10452 site:
http://www.esquarterly.com/bellagio/1987.htmlDec. 1987: Mattel Toys make a new addition to their Barbie range, California Dream Barbie, whose packaging includes a 5" flexidisc credited to The Beach Boys entitled "Livin' Doll", a Wilson/Landy Morgan composition. The track is actually a Brian solo performance based on an earlier song, "Christine".
The Barbie (Living Doll) flexi was mentioned a few times on this board, but apart from the above, no further info seems to be available.
And for the more serious collector: there's 2 variations of the flexi single: light blue with dark blue print, and dark blue with pink print
http://www.beachboys45.nl/USA-Regular-flexi.htm