He regularly wrote articles for newspapers and was interviewed about the early days, but never compiled a full biography. However, in 1928 he did publish privately a little booklet for distribution at a reunion of Vale of Leven players, and I have now digitised this for posterity. Click here to read it or visit my Publications page.
*EDIT It turns out the widely published date of 1863 for his birth is wrong! Arnott was, in fact, born in 1861 (albeit still on 12 May). Apologies for the confusion.