How much does capillary action contribute to blood flow to the human brain?
None. I have no idea what that video is talking about.

Capillary action of water happens when you have a thin tube and water likes to stick to the "edges." Blood vessels are already full of water, there is nothing for them to capillary up against: there is already water there, so there is no surface tension (there is no surface at all). Blood flow through capillaries is caused by the heart which creates a pressure gradient between the arterial and venous circulation, in the brain and everywhere else.



Cipolla MJ. The Cerebral Circulation. San Rafael (CA): Morgan &amp; Claypool Life Sciences; 2009. Chapter 2, Anatomy and Ultrastructure. Available from: https://www.ncbi.nlm.nih.gov/books/NBK53086/