How did James Boswell die?

Boswell died in the early morning of May 19, 1795, in his London apartment at Great Portland Street. He was buried at Auchinleck a few weeks later.

Boswell's final downfall began when, on April 14 of that year, he suddenly fell ill during a meeting at the club and had to be taken home to his lodgings. From this time on, until his death, he suffered from fever, shiverings, headache and stomach disorder. He remained confident of a recovery until the last, although unable to read, write or even leave his bed.

William Ober, in Boswell's Clap and Other Essays: Medical Analyses of Literary Men's Afflictions (1978), suggests that the actual cause of death was uraemia provoked by an acute recrudescence of chronic urinary tract infections. The book is available via AbeBooks.