To be potentially deductible, your education costs must either be required by your employer or by law to keep your job, or it must improve your skills you use at your current job.  As you can see, the operative terms are "keep" and "current" -  you were not eligible for this new job until you had completed the additional flight training

You cannot deduct the cost of any education that qualifies you for a new trade or business or is needed to meet the minimum requirements for your business, even if it meets either or both of the test.