Thanks for the response, that option is kind of off-limits for me though since I'm not a reloader.You want the slowest burning powder you can find (assuming you are willing to reload), so the powder is not completely burned by the time the bullet exits the muzzle. Or else blanks, where the absence of backpressure makes the powder burn slower.
If you google 'powder burn rate' you get several hits that list fastest to slowest powders, then you need to start digging around to find loads for 308 using those powders.
Easiest way to photograph it is to do it at dusk, and then set your camera to a small aperture, so you need a 1 second exposure (maybe 1/2 sec if you are coordinated), so you can push the button, then shoot before the shutter closes.
The other way is to go even darker, and use a Bulb exposure. Shoot while the shutter is open, and then manyally pop a flash before closing the shutter. You'll have to experiment with the aperture opening or sensitivity to get the muzzle blast at the right brightness, and then play with either the flash power setting of the distance between the flash and the people, so they are illuminated appropriartely as well.