Curious. "I speak Czech the best here" (my answer referenced in the earlier comment) IS among the acceptable translations, as is "I speak Czech best here." Maybe there was something else in your answer that Duo didn't like. (That's why it's always helpful if we copy/paste our complete answers into our comments.)
Umět means to have an ability, here to have a language ability. You know how to speak in the given language. Actually, it is not exactly the same as to speak. There are languages you may not speak at all, but you still can know them at a good level - like some ancient languages, read it and write it.
Or you can even be mute. And you can still say "Umím anglicky.".
But mostly when you know a language, you also can speak it. So you can say both "Mluvím anglicky." and "Umím anglicky.".
"Mluvím anglicky." can also mean "I am speaking in English." (right now, in case you can't determine the language)