Best option....send the highest end chief pilot an email saying something to the effect of:
Mr. ******,
I am a First Officer on the *****. I spoke with ****** about outside flying and he stated you are the person to make that decision. He explained the limiting factors are the commercial flight time limitations. I would like to instruct for a few hours here and there for ******. in ******. I assure you there will be no complications or issues as it relates to our company. I will ensure my flight time limitations will not exceeded under any circumstance and I acknowledge this airline is by far my first responsibility. With your permission, I would like to help out at ****** on a part time basis in my spare time.
Thank you for your consideration in the matter.
Respectfully,
Your Signature
He will respond.......
Approved, Let me know if there is anything else I can help with.
Then your covered