The average price per kilometre in a taxi is CZK 20 (EUR 0.75). The price for the trip from downtown to the Brno airport ranges from CZK 500 (EUR 18) to CZK 700 (EUR 25).
Unfair taxi drivers are everywhere, but their number in the Czech Republic is decreasing; to avoid the remaining ones, do not take a taxi directly from the street — rather call one by phone. Use only taxis that are clearly identified and ask about the price to your destination beforehand, if it is too high, do not get on.
You can use Liftago instead of a taxi. Download the Liftago app which matches you with a nearby driver to take you wherever you want to go.