I s a coffee maker a good way to purify water? Or....

Or do other chemicals in the water system such as chlorine and fluoride evaporate at around the same temperature?

The chlorine will be removed by boiling the water. The fluoride will not. Boiling won't remove most other chemical pollutants like lead or nitrates. Boiling will kill any bacteria present.
In short, boiling water to "purify" it is a waste of energy unless your water has a high count of pathogenic bacteria.