My buddy has a 72 Dart with a very similar motor as mine (318, xe268 cam, edelbrock 600 cfm carb, headers, 2.5" exhaust, flowmasters, MP dizzy, 3.21 gear [open], 2500 stall). It runs near to the same times that I do in my duster, which would be mid to high 14s usually.

When trying to do a burnout, he will stand on the brakes and bring the revs up. Once it reaches 2500 rpm, it will not rev higher, or spin the tires. When letting go of the brakes slightly, it still will not let the tires spin.

There should still be around 320-330 ft lbs of torque with this motor and it makes great power, even if the cam is a bit aggressive, so something should still be happening. Timing is set at 16 degrees initial and the motor runs flawlessly and efficiently.

Could the drums brakes in the rear be too tight, or is the open diff more of the issue?

Put a 440 in it

You can put a Posi Rear in it with 3:55 Gears and you will notice a big change. I would start there. It needs some gear in it if you want it to run.

Are you asking why the tires won't smoke?

1) Fairly low ratio in rear axle
2) Your buddy is powerbraking. One does that to get max torque on launch (best launch) and minimize wheel spin. If you want to do a smokey burnout best just to punch it, no brake from idle.
3) Probably have way less horsepower/torque than you think unless whole engine is optimized (dyno tuned/jetted) and you have great flowing heads.

Open diff should allow you easy burnouts regardless if you just punch it from idle (one wheel only). For fastest launch higher rear ratio and Sure Grip mandatory

Width/size of tires makes a big difference also. Wide = fast launch, skinny = smokey burnout.

Well this motor, like mine, ,makes every bit the power of a stock 340, about 270-280 hp, most likely 320-330 ft lbs. The gear isnt helping, but the 28" tall tire is probably more suited for hooking up. I tried the other day and it launches well.