I actually did this as an experiment over the weekend - I had a 14-day trial laying around from Halo 4, so I redeemed it and started Online from scratch on my Alt profile.
I recall actually having to be Level 8 before the Flight School unlocked - at least until the icon came up, anyway. I didn't use any exploits, so it took a couple of hours. Did Flight School, went from rank 8 to 12 and maxed my Flying - that took just under an hour and bagged me $200K (I can't gold the second-to-last mission - more to the point, I can't be bothered looking up then memorizing the One True Course) - with the cash I'd earned ranking up, that gave me $300K.
Did it again on second character. Actually made slightly more money, for a grand total of just over $700K for about 6-7 hours play, or roughly $100K per hour.
With the current mission payouts, you can squeeze in 4 back-to-back max payout Contact missions per hour. Solo, the most you're looking at is about $19.8K on Hard, so that's a little under $80K per hour - add an LSC car sale to that and you move into the $88K range - then again, take out ammo expenses and it pushes back down to the low 80's (unless you're a bullet-hose, in which case it could be significantly higher).
Final result: OP's method makes more money than grinding long contact missions. However, one downside is that all you are grinding is money, while your character does not progress in any other way (and you delete the second one, so all that non-money progress is lost as well). Another one is that ranking up those first few levels is fun the first time, but a total PITA the second, third, fourth time (someone above posted they made 8 million this way - they've done the grind to 6 (or 8) and the Flight School at least 32 times - I just don't have the stamina for that).
For my buck, I'd rather make $12K an hour less and progress my character than freeze him indefinitely while I grind and grind and grind for what only adds up to a big difference if you do it dozens of times (ie 10 hours of play for a difference of $120K - or about half the amount of money you could make on your main while you were ranking up the Flight School Alt).
Hmmm, perhaps the "Flight School" exploit isn't the goldmine it appears to be - it's almost like R*... knew we'd grind the sh*t out of it if it was and made sure that GTA: Online didn't become GTA: Lowbie Top Gun.