Howdy Kyle & welcome to the IAA forum.
You might also want to join the IAA for the Journal (and it’s past issues) which also offers lots of very interesting information about the wonderful world of ammunition in all its many various forms & uses.
Regarding your Kynoch headstamped 38-40, it could be either a shot loading or a blank. The weight should tell you, or perhaps if gently shaken you can feel the shot move or hear it. A bulleted load (lead or jacketed) for a comparison weight would also be of help (the case maker doesn’t likely mater) as the shot loading would likely be the same or heavier while a blank should be much lighter. This said, it seems you already feel it’s a shot load. My, somewhat educated, guess is that it would be loaded with #8 size shot, at least that is what I usually see on uncommon British shot boxes in 44 WCF or 38-40 boxes.
A number of companies made shot loads, for the XL chambered guns (usually, but not always, found with a long paper sabot usually with the paper color noting the shot size. Red, red with a black band, green, white, yellow & blue are the common colors, plus the normal length for Marlin’s, Colt Lighting’s, Winchesters & others.
As you perhaps know, Kynoch was a British maker & made quite a large number of US caliber / case types over the course of it’s history 1882 till the late 1960’s.
I think one of the back issues (perhaps early 1990’s?) of the IAA journal had a pretty complete list compiled by Don Amesbury of British loaded US calibers.
Hope this is of help.
Also please check out the show listings found on this site, then come meet other collectors & get some new specimens for your collection.
Lots of us have lots of extras in the inexpensive price range.