Do I qualify for the American Opportunity Tax Credit if I bought college material with a stipend from my military college benefits?

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Yes. 

"Example: You have returned to college and are receiving two education benefits under the latest GI Bill: (1) a $1,534 monthly basic housing allowance (BHA) that is directly deposited to your checking account, and (2) $3,840 paid directly to your college for tuition. Neither of these benefits is taxable and you don't report them on your tax return. You also want to claim an American opportunity credit on your return. Your total tuition charges are $5,000. To figure the amount of credit, you must first subtract the $3,840 from your qualified education expenses because this payment under the GI Bill was required to be used for education expenses. You don't subtract any amount of the BHA because it was paid to you and its use wasn't restricted."

https://www.irs.gov/individuals/tax-exclusion-for-veterans-education-benefits#:~:text=Payments%20you%20receive%20for%20education,the%20VA%20are%20tax%20free.&text=Neither%20of%20these%20benefits%20is,total%20tuition%20charges%20are%20%245%2C000.