A charge action has nothing to do with the run action.
Running is a full-round action where you move 4 times your speed (3 times for heavy armor, 5 times with the Run feat).
Charging is a special attack action that allows you to move up to twice your speed and then make an attack.
Charging makes no reference to running, or even being on the ground. Swimming creatures can charge. Nothing says flying creatures
can't charge, so they can. Flying creatures also have the
additional option of making a dive attack, which is
like a charge with some extra requirements and benefits.
I've read "fly" spell.
It states that while descending your speed is doubled.
(I know I'm using 3.5 links instead of PF, but the d20srd is much easier to link to and the wording is the same anyway.)
"(...) The subject can fly at a speed of 60 feet (or 40 feet if it wears medium or heavy armor, or if it carries a medium or heavy load). It can ascend at half speed and descend at double speed, and its maneuverability is good (...)"
Is this a senteces ( In your opinion ) which can accord a player to charghe while flying?
This is irrelevant to charging. Those are changes to your speed, which is a stat. Charging is an action where you move twice your speed. Getting your speed doubled is not the same thing as charging twice your speed.
(I know the topic is PF, but d20srd.org is much easier to link to and the wording is the same anyway.)