529 and american opportunity

You are "allowed" to do that, the distribution may also be applied to Room and Board which would make it non-taxable and also free-up expenses for the credit.

Enter the 1099-Q and 1098-T into the TurboTax program and select that the program "Maximize my Credit"

If you are a dependent student, the taxpayer that claims you gets the credit. 

IRS Pub 970 

Q.  I paid 100% of college tuition and expenses with 529.  Can I now "move" and pay taxes on $4000 of that withdrawal to qualify for American opportunity credit?

A. Yes.  You are allowed to allocate your expenses to the four major education tax breaks*, as needed, for the best result.  So, yes you can move paid expenses from the 529 distribution to the American opportunity credit. When you do so, only a portion of the earnings (box 2 of the 1099-Q)  will be taxed, not the whole $4000. See example below.  Allocating some expenses to the tuition credit is an exception to the 10% penalty, so only tax will be due.

Room and board is  only a qualified expense for the 529 plan distribution.  You cannot claim the credit or keep a scholarship tax free by allocating R&B, but you can move/allocate R&B to the 529 distribution.  

If your student has scholarships, allocating expenses away from the scholarship is another option, and usually the best option.  This makes $4000 of the scholarship taxable to him. But, if that is his only income, no tax will be due. Even if he has some other wage (earned) income, no tax will be due up to $13,850. You can only do this if the scholarship is not restricted to paying for tuition.  

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Qualified Tuition Plans  (QTP 529 Plans) Distributions

General Discussion

It’s complicated.

For 529 plans, there is an “owner” (usually the parent), and a “beneficiary” (usually the student dependent). The "recipient" of the distribution can be either the owner or the beneficiary depending on who the money was sent to. When the money goes directly from the Qualified Tuition Plan (QTP) to the school, the student is the "recipient". The distribution will be reported on IRS form 1099-Q. 
The 1099-Q gets reported on the recipient's return.** The recipient's name & SS# will be on the 1099-Q.
Even though the 1099-Q is going on the student's return, the 1098-T should go on the parent's return, so you can claim the education credit. You can do this because he is your dependent.

You can and should claim the tuition credit before claiming the 529 plan earnings exclusion. The American Opportunity Credit (AOC or AOTC) is 100% of the first $2000 of tuition and 25% of the next $2000 ($2500 maximum credit). The educational expenses he claims for the 1099-Q should be reduced by the amount of educational expenses you claim for the credit.
But be aware, you can not double dip. You cannot count the same tuition money, for the tuition credit,  that gets him an exclusion from the taxability of the earnings (interest) on the 529 plan. Since the credit is more generous; use as much of the tuition as is needed for the credit and the rest for the interest exclusion. Another special rule allows you to claim the tuition credit even though it was "his" money that paid the tuition.
In addition, there is another rule that says the 10% penalty is waived if he was unable to cover the 529 plan withdrawal with educational expenses either because he got scholarships or the expenses were used (by him or the parents) to claim the credits. He'll have to pay tax on the earnings, at his lower tax rate (subject to the “kiddie tax”), but not the penalty.

Total qualified expenses (including room & board) less amounts paid by scholarship less amounts used to claim the Tuition credit equals the amount you can use to claim the earnings exclusion on the 1099-Q. 
Example:
  $10,000 in educational expenses(including room & board which is only qualified for the 1099-Q)

   -$3000 paid by tax free scholarship***

   -$4000 used to claim the American Opportunity credit

 =$3000 Can be used against the 1099-Q (on the recipient’s return)

Box 1 of the 1099-Q is $5000

Box 2 is $2800

3000/5000=60% of the earnings are tax free; 40% are taxable

40% x 2800= $1120

There is  $1120 of taxable income (on the recipient’s return)

**Alternatively; you can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses, including room & board (even if he lives at home) to cover the distribution. You would still have to do the math to see if there were enough expenses left over for you to claim the tuition credit. Again, you cannot double dip!  When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records, in case of an IRS inquiry.

On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 

***Another alternative is have the student report some of his scholarship as taxable income, to free up some expenses for the 1099-Q and/or tuition credit. Most people come out better having the scholarship taxable before the 529 earnings. 

*Tuition Credit, Tax free scholarship, QTP (529) distribution and maybe Savings Bonds.