to be precise the "whenever you make a Charisma check when interacting with dragons, your Proficiency bonus is doubled if it applies to the check." in most other text when it mentions a type of check it will say something along the lines of "Charisma (Persuasion)" but the text just reads "charisma check" witch makes me think it is just for flat charisma checks witch you don't add proficiency bonus to so double 0 is still 0.
to be precise the "whenever you make a Charisma check when interacting with dragons, your Proficiency bonus is doubled if it applies to the check." in most other text when it mentions a type of check it will say something along the lines of "Charisma (Persuasion)" but the text just reads "charisma check" witch makes me think it is just for flat charisma checks witch you don't add proficiency bonus to so double 0 is still 0.
Persuasion is a type of charisma check, as is deception, intimidation, and performance, not to mention tools can sometimes have an ability check.
Basically if it is not a save (saves are not checks), it adds CHA, and deals with dragons, you can double proficiency.