The Fidelity bonus can be gamed by moving small deposits into and small withdrawals out of your new brokerage account. If this is the approach you want to take, kyunbit's advice may make sense.

However, if you want the least amount of hassle, make a large enough deposit at Fidelity to earn your sign-up bonus, wait for the miles to post, and move most of your money into BankDirect afterwards. Most of the AA miles earned at BankDirect are based on your average balance held at BankDirect. That means you want a large balance to sit there over time in order to maximize your miles. Every time you move money out of BankDirect and into Fidelity, you are negatively impacting your BankDirect earnings for the month. The only risk you take with this latter approach is Fidelity somehow taking back your miles because you didn't leave your initial deposit with them, but I don't believe I've heard of anyone reporting this in the past.