The only copy of a Mariposa Folk Festival LP I've been able to track down is from 1976; there's a copy on Ebay Here which gives full track details - but no PB & no Flying Cloud! Did PB ever sing Flying Cloud? A quick search reveals a blank on that too...

As for hearing PB, there's a couple of things on YouTube, including THIS in which PB's rendering of The Fox Jumps Over the Parsons Gate (1970) is married with the images from Randolph Caldecott's book of the same name (1883) - by all accounts a seminal influence on the young PB!