According to the Online Etymology Dictionary, the term griffin/griffen/griff/griffe was used "with uncertain connections, in mid-19c. Louisiana to mean "mulatto" (especially one one-quarter or two-fifths white) and in India from late 18c. to mean "newly arrived European.""

It is a racial classification, and given the use of Magazine Street in the handbill there, I'd assume New Orleans, in which case the use of the term makes perfect sense.

To the best of my knowledge, a "griff" was a racial classification, like a "mulatto" or a "quadroon". It never had a very precise definition, but generally reffered to a black slave with a lighter brown skin, but no so light as a mulatto, implying less than 50% white ancestry, but more than 0% white ancestry. As always, skin color was used as a proxy for ancestry, which as we all know is not a very precise or accurate way of gaguing these things.

More information can be found in "The Slave Trader, the White Slave, and the Politics of Racial Determination in the 1850s" by Walter Johnson, published in the Journal of American History, and available online here: http://www.uvm.edu/~psearls/johnson.html