Yes, you can use it for this route! However, if you only make this journey on your first (or last) travel day, I'd advise you to buy a seperate ticket. You have two options:

• DSB train Copenhagen Airport - København H
• Metro Copenhagen Airport - Kongens Nytorv (or whatever metro station suits you best)

As @Mattheas  said this trip would need a travelday of your flexipasses and if it´s your only trip on that day i recommend to use the local offers as mentioned above.

Thank you