The SVT40 DOES have a fluted chamber but the flutes are only cut at the neck (front) of the chamber and stop unlike the CETME where the flutes are cut the full length of the chamber and clearly visible. When you fire the SVT rifle, the flutes MUST be clean so that they allow some of the gas to "float" the spent cartridge out. If those flutes are not clean, then the rifle is relying on the extractor claw, alone, to pull out the spent cartridge while it's probably wedged in there pretty good.
It's tough to see the flutes but if you look hard with a good light you can see them clearly cut into the front of the chamber as it heads into the neck. You can't see them from the muzzle end. And, you should definitely see "flute marks" on the brass/steel when it comes out. Examine a spent brass and If you don't see them, that's a good sign you've got impacted flutes that need cleaning.
Adding gas may help but there's a good chance you could damage the extractor claw more than likely.
First, clean the chamber and check for burrs. Second get a big brass brush in there and scrub forward and backward with some good bore cleaner. I use a small shotgun brass brush, myself, and work from the receiver end. Just keep rubbing in and out keeping the brush soaked with cleaner. If it's hard and impacted you may want to try some foam cleaner and let it soak there for a bit and then go at it again. Once you clean it, you'll find the rifle runs a lot smoother and the brass will have those telltale black soot marks from the flutes clearly on them after firing. Lacquer from Soviet steel cartridges may also be clogging them.
Until I checked all that out, I wouldn't shoot it again. Good luck!
Rome