I teach English in China, and the textbooks have never been a problem. The dialect differences between AmE and BrE with regard to lexis and grammar are very slight. It's a non-issue. The same holds true for pronunciation: Chinese do more business with non-English speaking European countries and Asia than they do with English speaking countries. So it doesn't matter which accent you use, the challenge will be and presently is for Chinese to be able to understand English accents from around the world (e.g., Russian-English, Indian-English, French-English, and so on). The division between AmE and BrE, frankly, is part of the past.
Just my two cents.
Student or Learner