In a nutshell: it's complete rubbish and the people propagating such claims are usually advancing a political/racial agenda.

This is an idea that's been kind of lurking around in some, well, less tolerant elements of society for a while, but really started to gain some traction in the early '90s when the Nation of Islam published the absolutely, horrendously bad The Secret Relationship Between Blacks and Jews. The Secret Relationship is basically a hyperbolic anti-Semitic tirade dressed up as a work of rigorous scholarship; two very prominent and respected historians of slavery, David Brion Davis and Seymour Drescher, have penned critiques ripping the idea and book apart.

Probably the most accessible and well known refutation of the notion though is Eli Faber's Jews, Slaves, and the Slave Trade: Setting the Record Straight (New York: New York University Press, 1998). It's not just a critical refutation; it's a very good piece of history in its own right that demonstrates quite clearly there was minimal Jewish involvement in the slave trade, and slavery in general. Even when Jewish people were involved, Faber observes that they tended to be less intimately or extensively involved as their non-Jewish counterparts.