I don't know about the fluoride...I am pretty sure that the tap water where I live is not flouridated (unlike most of the US). But for chlorine...you can actually buy chemicals which are designed to break down chlorine, chloramines, ammonia and heavy metals. They are generally meant for fish tanks...because these things are toxic to fish too! You only need a tiny amount...a tablespoon is enough for 60 gallons...then you slosh the water around and it breaks down all the harmful chemicals and leaves the water smelling surprisingly sweet (maybe because our noses are designed to help us sense whether water is good or harmful)?
Before I started doing this, I would always feel terrible after taking a shower or bath...fatigue and total brain fog. But since I started doing this, I can actually take a bath and feel good afterwards! So it definitely works for chlorine. However, I don't think it would have any affect on the fluoride.