Rifle is an AR10 308 with a 16" Ballistic Advantage barrel. This pic is a PMC 150 grain soft point, but it's happening to other brands as well.

Try different magazines. That looks likes scratches and rotation happening while sliding in/out of the mag.

I assume the photo is a fired case? What do the chamber walls look like?

Looks like a problem with the end of the chamber.

Seems Ballistic Advantage's QC is slipping... I made a post and there have been others lately reference quality, or a lack thereof.

How old is the barrel? Was it a recent purchase.

Either way, BA will take care of it, most likely swap out barrels for you. I'd contact them ASAP.

Tnx for the tips. Yes, new BA barrel. Was going through a barrel break-in period. Chamber looks good. I only used one magazine, so will try that next. In the mean time I'll contact BA for some advice.Tnx.

BA responded to my inquiry. I think they're dumbfounded. Something is causing the case to spin more than what you get during a feeding cycle, which doesn't rotate much (a lugs worth?). I don't think it's a magazine issue but will try a couple others the next time out. It's a Magpul polymer mag and won't dig into the brass like this. When I swapped barrels I didn't check for head space issues since I didn't want to spend the money on the only 308 I have. No problems cycling and no over pressure issues that I could identify. So anyway, I await BA's evaluation, and proceed from there. It's just crazy, I say, just crazy. LOL

Even if the casing was locked onto the bolt (and rotated the same distance as the bolt) as the bolt locked and unlocked into the extension it wouldn't account for the marks. The marks/ lines on the case extend longer around the perimeter of the case than the bolt rotates.
Since you say the chamber looks good I assume there isn't an obvious group of lines that imprinted onto the case as it expanded against the chamber walls. There isn't really any other explanation I can think of that would explain multiple rounds ending up like this. Could something have been stuck in the chamber and now it's gone?

just curious, if you charge a round, extract the unfired round.  does it have the same marks?  at the entrance to the chamber, is the feed cone smoothly rounded?  or sharply beveled?  if sharply beveled, might be those edges at the feed cone.  just grasping at straws.

Tnx for all the tips. I sent a bore scope video and chamber video and pics to Ballistics Advantage. They're not sure what's going on with it. They sent me an RMA and label and they're going to inspect it. They have been great to work with. I didn't even buy the barrel directly from them, but through Primary Arms (big sale). If they say the barrel is within specs, I guess they'll send it back and tell me to look elsewhere for an issue. I dropped a new 308 cartridge in the chamber on two 308 barrels, and they both looked identical. My impression was the cartridge in the BA barrel was a scunge lower in the bore, but it's really hard to tell or measure.Very close. Sooo, I bought a go/no go gauge $et, but the barrel is gone now, so alot of good that did me. BA responded and acted so quickly it threw my timeline off. Bastards. LOL. I still can't imagine how a cartridge could spin like that. My evaluation suggest the the spinning comes from firing and the case is being spun by the bullet when it first hits the lands. I guess this could happen if there's no 'jump' from the seating depth to the lands. Reloading 101? You'd think that would be indicative of a seating issue, which is why I bought the gauges. On the other hand, with brass expansion, you'd think there's no way it can spin like than in the chamber after firing. I need more Scotch!

One thing I can tell you is that it is not being caused by the case turning in the chamber when the bullet engages the rifling.  The pressures involved in unseating the bullet stick the case to the walls of the chamber so that it is not going anywhere, let alone spin like a top.  As to the scratches, rough chamber would be my guess and they are getting ironed into the case when it expands to fill the chamber, but it certainly is not from the case spinning when the bullet engages the rifling.