Maybe decay. Teeth should not chip while flossing. If this is happening, it may be a sign that there's something weakening your teeth enough, that simply flossing will break the apart. It could be decay, it could be an old, failed filling. What you need to do is see your dentist asap.
Teeth chip w/floss. Dental chipping or breaking is usually due to breaks in the tooth enamel, the hard "shell" that protects/insulates the tooth. Chips/ breaks may be caused by high starch/carb diet, medications, carbonated drinks, dry mouth, reflux and genetic anomalies that affect the quality of teeth/enamel. See your dentist for a check-up and cleaning. Brush & floss twice daily and reduce foods that predispose.
Some dental problem. First, it's great that you are flossing. If something breaks, chips, loosens or if the floss gets caught or frays when flossing, it indicates that something is wrong. It's better to floss and have this happen then to not floss and not be aware of some dental problem before it's too late and you have a bigger problem. See a dentist to find out what's wrong and what needs to be done to correct this.