私はテキストを買ってますが、流れてくる英文をテキスト見ずにまず書き出しています。

、。

I've bought the textbook, but I first write out the English sentences as they come without looking at it.

Literal

I [topic-は] textbook [object-を] buying-[progressive-てます][but-が], flowing-come English [object-を] textbook look-without first write-out-[progressive-ています].

流れてくる 'flowing/coming through' — audio being played or broadcast. テキスト見ずに 'without looking at the textbook' uses the literary ずに (negative continuative, equivalent to ないで). 書き出す 'to write out, to transcribe' is a compound verb. The sentence describes a dictation study method.