The number quoted by Bill Browder, an American-born British financier, is $200 billion:
> I estimate that he has accumulated $200 billion of ill-gotten gains from these types of operations over his 17 years in power.
This is from Browder's testimony to the United States Senate, he is the CEO and co-founder of Hermitage Capital Investment (formerly the largest foreign portfolio investor in Russia).
The $300 billion figure may have been a typo, or misremembered, but I didn't find another source for it.