Khaman Maluach had 11 points and 14 boards for the Blue Devils (2-0). Kon Knueppel added 15 points, Tyrese Proctor tallied 14, Sion James had 12 and Caleb Foster scored 11 for Duke.
"It's almost a situation where you have to play well because you know there's somebody behind you waiting to play as well," said James, a graduate guard. "But it's an unbelievable thing - it's great for culture and great for chemistry when you know the guys behind you are still cheering for you and still want you to go. I'm coming off the bench, but I love when Tyrese gets hot. I love when Caleb gets hot. These are the guys who are taking my minutes, in theory, but that's a culture thing. I love when those guys get going and that's what makes us better as a team."
Flagg dunked a lob from Proctor to complete a fast-break alley-oop after James stole the ball from Army. Flagg's two-handed transition slam ignited a 29-7 Duke run over the next 13 minutes.
Duke dominated on the glass and inside, outscoring the undersized Black Knights 36-18 in the paint and 17-7 on second-chance points. The Blue Devils outrebounded Army 50-32.
"I'm getting there one step at a time with the college game. It's a different game, but I feel like I'm catching up every game," freshman center Maluach said. "I knew it was going to be different and I wasn't scared of the change, so I knew a lot of stuff was going to be different and I had to just adapt to it. Being a college athlete is great and I'm just enjoying and embracing every moment while I'm here."
For Army (1-1), Jalen Rucker scored 17 points, while Josh Scovens added 16 points and seven rebounds.
Former Army and Duke coach Mike Krzyzewski, a West Point graduate and the all-time winningest coach in the history of Division I men's college basketball, sat courtside at Cameron Indoor Stadium with his wife, Mickie.
"To play Army on Veteran's Day weekend really means a lot to us," said Duke head coach Jon Scheyer. "What they stand for, what those kids do, the commitment that they've made to our country means a ton. They're a tough, disciplined, hard-nosed group. I was happy with what we did, overall. A lot to clean up, a lot to build on. Particularly the first-half defense, to hold them to 20 points was great. Cooper (Flagg) and Khaman (Maluach), to have double-digit rebounds in the first half. Just need to keep building."
Flagg only played 25 minutes and seemed to be battling cramps on the sideline in the second half, using a massage tool on his hamstrings and guzzling Gatorade. Against more marquee opponents, Duke will need the preseason AP All-American to be available for the entirety of the game.
Duke made 17 3-pointers, more than the Blue Devils made in any game last season.
The Blue Devils face their first major conference opponent of the season Tuesday, taking on No. 23 Kentucky in Atlanta the same day the Black Knights return home to host Division III Mount Saint Mary.
The Associated Press contributed.