Hi Tim,
In the later history of belt drive motorcycles in the UK (1910-mid 1920s) most belts were "solid" V belts with a joiner. There were exceptions - a very complicated and expensive link belt by Whittle for example - but most makers built pretty ordinary V belts, albeit with their own features (canvas, rubber, strengthening, etc), and joiners too.
In the US, flat belts were most common and chain drive came in much earlier - almost universal by the mid teens.
I don't know when the Brammer-style "link" belt became popular in the UK, but it was in the "restoration age": i don't think it was around in the period when belt-drive bikes were new?
These days you have a choice of belts, but as usual nothing is easy.
1. Modern industrial V belts, available in a huge range of sizes, are fantastic. If you have a frame with removeable seat stays, an endless V belt is a game-changer. If you can get exactly the right length it will run smoothly, never slip, and last forever.
Beware, however, cutting an industrial belt and fitting a joiner. Modern belts often get their strength from a kevlar (?) "rope" that runs through the belt. There is no strength in the belt to support the screw that fastens the belt clip, and it will pull out. Old belts used multiple layers of canvas.
2. You can/could buy cut-to-length V belt designed to take a fastener: we bought some fabulous stuff out of the USA about 20 years ago and I'm still using it. The UK version was green "vari rope". It was always rubbish and wore quickly, but was useable.
3. The final possibility is the "link belt". The Brammer version often used in the UK looks pretty good and seems to work OK, but some of the other versions are brightly coloured and plastic-looking, but seem to work OK. Personally I don't like the look...
If your frame unbolts, and you want to ride the bike, I recommend a modern V belt of the appropriate width and length. Cheap and trouble-free once setup. If you have a transmission specialist in town, they can help to determine the correct belt.
Leon