I have plaque or tartar behind the back of my bottom front teeth. I was flossing and the bottom of my front lower tooth chipped a little bit. Bad?

See Dentist. See dentist about chipped tooth. Sounds like you need a professional dental cleaning also.
See a dentist or RDH. Once plaque has hardened into calclulus, you need to have it removed by a dentist or RDH. For your chipped tooth also see a dentist for consultation and restoration if needed.
Not Good. Not good, BUT, you might have only dislodged a piece of the buildup (calculus/tartar) and not your actual tooth. Likely that is the case. See your Dentist to evaluate and treat if you did chip the tooth, and get the cleaning done to remove the calculus, and get specific home care tips to prevent the buildup in the future -- you can do it. Good Luck.