I purchased a dual GFCI/CAFCI circuit breaker to place on my circuit that contains only smoke, CO, and heat detectors inside my house. Is there anything wrong with this or can I install it to have both types of protection?
A smoke alarm can be AFCI and or GFCI protected so the answer is yes. Code exempts fire alarm systems installed to code NEC 210.12.A.6. from AFIC requirements. My state also exempts Fire alarms from GFCI requirements. The risk to the system tripping out is greater than the chance of a fire or shock from the system. I totally agree with @Harpers comment.
I used a gfci/afci dual breaker, simply because I had a free one already. Code allows it (though I agree that it's better to not have it)