"Became" would have been my first, most instinctive choice, but basically either that or "was made" is acceptable, at least from a linguistic point of view — from a theological point of view, I guess it could be debated world without end. However, the Douay-Rheims Bible, which was translated literally from the Vulgate, translated et verbum caro factum est in John 1:14 as "and the word was made flesh" and the KJV, which was translated from the original Greek, reads the same although the Greek verb, unlike the Latin, isn't technically a passive form of a verb meaning "to make" (In Greek, it's as if the deponent fieri had its own forms in all tenses).