To get from Zurich to the Czech Republic on the cheap I would go to the Deutsche Bahn website and check for special offers from Zurich to Germany. There is a special offer called Europa-Spezial Schweiz (Europe-Special Switzerland), it is valid on selected trains from any point in Switzerland to any point in Germany.
This is how to do it:
First look up a connection that allows you to go Zurich-Prague-Brno via Germany on www.bahn.de. There should be a train from Zurich to Munich and then a train from Munich to Prague. Print those connections out or write everything down. Check where the train from Munich to Prague stops, write that down too.
Second step is to search for the special offer, look up connections from Zurich to Munich, Regensburg or even better from Zurich to one of the border stops between Germany and the Czech Republic (Bayrisch Eisenstein, Cheb or Furth im Wald). Try to get as far as you can to the Czech border with this special offer. (Take a look at a map.)
Ideally you would take the train from Zurich to Munich and then the train from Munich to Prague, but you'd have a special offer ticket that goes as far as the German-Czech border (Bayrisch Eisenstein, Cheb or Furth im Wald). You'd buy a ticket on the train from the Czech conductor for the remaining part of your trip, either to Brno or to Prague.
This is not a fast way to do it, but if you can get the special offer for 39 EUR to the Czech border it will be very cheap. You'll pay around 15 EUR to get from the Czech border to Brno via Prague, so everything will be around 55 EUR total.
With paying 55 EUR for Zurich-Brno and 25 EUR for Paris-Amsterdam a Eurail pass would be a total waste of money.
BTW, if you go via Vienna because it is faster note that there are other special offers on this route too. Let me know if you go this way, I'll gladly explain.