This paragraph is purposefully written to sound confusing and is meant to be humorous. It is a story of the only court case that ever perplexed Judge Taylor. Basically, the case was between two families, the Cunninghams and the Coninghams (both poor families of Old Sarum).
Though they were two completely separate families at first, eventually they began marrying one another. When Scout says "the spelling of the names was academic" she is likely referring to the fact that both families were rather uneducated (and likely illiterate). This probably means there was a variety of ways either name ended up spelled on official records and documents. It didn't pose a problem until one member of one family decided to dispute the ownership of land with the other family, likely citing a name misspelling as the reason for the confusion over who owned the land. At any rate, Judge Taylor eventually threw the case out of court calling it "champertous connivance." As a legal term, this means one party is working with the other party in order to share in the proceeds. The term is humorous here, because Judge Taylor is basically saying in a way that no one would understand, "You are all crazy. I hope you are happy that you've had your public opportunity to say your piece, now get out of my courtroom."
Again, it is purposefully confusing because the case itself was ridiculous and confusing. Read it with a tone of nothing but humor, and understand the point is to show that only something as extreme as that case could get Judge Taylor to lose his sense of professionalism as a judge.