A burr at the barrel port is a common issue with many inexpensive barrels. It can be fixed with a dowel wrapped in steel wool or wet/dry sandpaper, or with a 3/32" to 1/8" diamond ball.
I feel like I need to define the terms I used above so there will be no misunderstanding about the process I am suggesting. The beauty of having a common vocabulary is that is saves having to describe in detail the appearance of a part or area. Since I do not share the jargon of the airgun community I will describe in detail what I mean:In firearms, once you pass the barrel breech (the part of the barrel opposite of the muzzle where the ammo is loaded) there is a chamber which is made up of 2 sections one called the freebore which is cylindrical that matches the cartridge casing and the other is the leade which is conical and guides the projectile into the rifling. Most airgun barrels only have a freebore/chamber and tend to not have a leade which is why I recommend cutting one into the rifling. When I suggest brunishing the freebore I mean that part of the chamber which is cylindrical. When I say cutting a leade I am refering to making a bit of a conical transition from the freebore to the rifling. If the chamber is a leade what do I call the leade? If the action is the breech what do I call the breech?