The best way to transfer knowledge is for the people who need the knowledge to work with those who have the knowledge.
Whilst the knowledgeable people may not have the time to work on documenting their knowledge themselves, they may already be spending some of their time explaining to others what to do and how to do it.
Even if the knowledgeable people had the time to write up their knowledge, it is not necessarily the case that the documentation they produced would be of use to the less knowledgeable people. It is surprisingly easy to miss out important 'obvious' information when trying to impart knowledge.
By making the knowledge transfer more explicit and co-operative, and having the users of that documentation write it so that they can understand it, you could both ease the burden on the knowledgeable people and get more information transferred.
If the knowledgeable people are really pressed for time, you could ask the people who need that knowledge to write up what they understand now, and then have the knowledgeable people proof-read and correct any understandings. This could substantially speed things up, and could also help identify areas where the knowledge is lacking.
As an example of this, I work on scientific software. Neither I nor the scientists I work with could alone document much of the software I write. I could explain what my software does and even why it does it that way, but it's the scientists who need to write documentation on why and how visiting scientists might want to use it.