This tradition of blending chicory with coffee is not unique to New Orleans alone. It's been done in Canada, France, India, and Southeast Asia, both because the flavor was preferred and also to stretch out supplies of coffee (which was more expensive and often scarce).
The flavor of chicory coffee is...unique. Personally, I thought it was less robust than the coffee that I'm used to. Lighter in body and a touch more acidic. There was a citrus quality that gave the coffee a brightness. Other people describe this as a bitter chocolate flavor.
I liked it black, but adding a generous pour of milk definitely helped mellow out the flavors. The famous Café du Monde French Market Coffee Stand recommends serving it au lait style, half chicory coffee and half steamed milk. With a beignet on the side, of course.
For another perspective on chicory coffee, take a look at Chez Pim's visit to Café du Monde:
• Café du Monde’s beignets: how many ways can you say fabulous? from Chez Pim
Do you like chicory coffee? How would you describe its flavor?
(Images used with permission from Pim Techamuanvivit of Chez Pim)