Can I claim the mileage to and from the airport for my fly in / out job?
Most likely not. CRA considers any travel to get to your place of employment to be a "personal" expense. If you are required by your employer to fly in and out of your workplace, travelling to the airport is considered "travelling to and from work".
If you were eligible to claim "Travelling Expenses" as an Employment Expense deduction, CRA specifically states that motor vehicle expenses do not qualify as seen in the following document.