What are some canonical or seminal corpus linguistic studies using the Brown Corpus?

The key early works based on the Brown corpus are, of course, Kucera and Francis' 1967 work "Computational Analysis of Present Day American English" and the American Heritage Dictionary. It's greatest long-term impact was in inspiring the creation of other corpora like LOB (Lancaster-Oslo-Bergen) which then led to some innovative work on grammars.

You will find very little use of the Brown corpus in modern corpus linguistics research. There are simply too many far better resources. A modern respectable corpus of written language will start at 100 million tokens (as opposed to Brown's 1 million) and try to go much higher. It is sometimes used for teaching purposes and I still see it used for some basic frequency work in non-specialist works - this is probably in part because of its easy accessibility.