The late Peter Kennedy recorded Charlie Scamp, so those recordings are unavailable at the moment. One song, 'Atching Tan Song', is transcribed in Kennedy's Folksongs of Britain and Ireland. If you don't have ready access to that, I can copy it for you.

'Ken Thompson: A Kentish Man and His Songs' isn't a book, but a two-page article by Fran and Geoff Doel that appeared in English Dance and Song, 54, 2, 1992. Again, I can sort you out a copy.

Since you've checked the Roud Index, you'll know about Mike Yates' Kent recordings, some of which are available from Musical Traditions. All the booklet notes are available at the MT website.

Quite a few collectors got stuff in Kent, though the county wasn't researched systematically as (for example) Dorset, Hampshire and Somerset were in the early years of the C20. Still, there are various transcriptions in the Journal of the Folk-Song Society and the like, so if there's anything particular you're interested in seeing, let us know.

The set of 'Death and the Lady' in The Penguin Book of English Folk Songs / Classic English Folk Songs was found in Kent, incidentally (though some of the verses were added from other versions).