No you and your son cannot double dip. you cannot both use the same expenses to claim a tax benefit.
But you can split up the expenses to achieve the best over all benefit. Depending on your tax situation, it usually best (for him) to claim the tuition credit first. The American Opportunity Credit (AOC) is 100% of the first $2000 of Tuition and 25% on the next $2000. The AOC is also 40% refundable. The Lifetime Learning Credit is 20% of tuition paid, up to $10K.
Example:
$10,000 in educational expenses(including room & board)
-$3000 paid by tax free scholarship
-$4000 used to claim the American Opportunity credit
=$3000 Can be used against the 1099-Q
Box 1 of the 1099-Q is $5000
Box 2 is $600
3000/5000=60% of the earnings are tax free
60%x600= $360
You have $240 of taxable income (600-360)
