Is it seen as an advantage to be fluent in Czech when trying to teach in Prague? Or is it okay to only know English?

Answer

Typically, knowing the local language doesn't hurt and is sometimes seen as advantage, but it's not a requirement. In other words, knowing Czech -- even just minimally -- could help you get a job (and function as an expat) but it won't disqualify you from teaching English.

As someone who knows absolutely zero words of Czech I can say from personal experience that it is not necessary to speak the language to get by in the Czech Republic. Especially if you are in a major city such as Prague you will find many English speakers.

However, of course any local words you can pick up will help you go further to make connections and succeed in work.