Simply put, if I give a flier an action to charge can I carry someone with the charge movement? If so do I apply the half move for charge first or the -2 for carry first?

Replace then modify.

so you have 10?

5 then -2 for 3.

Anytime a character moves (the action has to use the word "move") you have the option to use the carry ability if you have it. The standard modifiers for carrying will still apply.

The general rule for replacements (things that double or cut in half are replacements) and modifiers (something that uses a plus or minus), is you apply the replacement first and then apply modifiers to that new value.