Ann has taught university level Film classes and has a Master's Degree in Cinema Studies.
There's no words here to differentiate between between the two dialects at all, so it passes for both. Potentially, "University" and "Master's Degree" might have a different meaning between the two countries, but neither by itself points to any particular dialect. It's okay to use this in the context of American English, for sure.
There is no way to tell whether this statement is American or British English, because of the context.
You might find this surprising, because this sentence uses a word where there is a big distinction between the two dialects. In specific, British English typically uses the word "film" while American English would typically call it a "movie". Likewise, British English will call the building a "cinema" while American English uses the phrase "movie theater". The issue here, however, is that this sentence is referring to an academic setting. In academia, both British and American English will use the words "film" and "cinema".
As a side note, this is one reason why Americans often have the idea that British people sound more intellectual-- many common British English words are also American English words, just exclusively in the academic register.