King James Version Text

The source document or revelation that became the Book of Abraham could have easily contained similar material so Joseph Smith included it.

The only description given by Joseph Smith regarding the translation process was that it was performed by the “gift and power of God.” Some accounts state he may have used the Urim and Thummim (likely the seer stone). This would not prevent the inclusion of other previously written inspired texts. 

The Church's 2014 essay on the Book of Abraham explains why the text imitates the King James Bible:

"Much like the Book of Mormon, Joseph’s translation of the book of Abraham was recorded in the language of the King James Bible. This was the idiom of scripture familiar to early Latter-day Saints, and its use was consistent with the Lord’s pattern of revealing His truths 'after the manner of their [His servants’] language, that they might come to understanding.'"

Latter-day Saint scholars have posited a number of plausible explanations to account for the quotations and paraphrases of Genesis in the Book of Abraham. There are too few known details to ascertain the precise details.  Theories include:

Three Latter-day Saint scholars posit that the Book of Abraham and Genesis share common sources. "Although the book of Abraham has many additional details not found in the account of Abraham's life in the Bible," Richard D. Draper, S. Kent Brown, and Michael D. Rhodes write, "the close similarity of language of some of the verses contained in both the book of Abraham and Genesis" have led them to speculate that "Moses may have used [the Book of Abraham] as one of his sources in the writing of Genesis."

The Genesis material was redacted into Abraham's own account as a later documentary source during the transmission of the text.

The Book of Abraham is a Greco-Roman pseudepigraphon that is the product of Egypto-Jewish syncretism that draws from the book of Genesis and the same milieu that produced other ancient apocryphal texts about Abraham.

The text of the Book of Abraham was received independent of any physical documents (ancient or modern), and is purely a revealed text by Joseph Smith that expands upon Genesis in something of a prophetic, midrashic exploration of the life of Abraham.

If one assumes that the Book of Abraham was word-for-word written by Abraham sometime circa 2000 BC, then these anachronisms pose a problem. If, however, one accepts the likelihood that scribal emendations were made to the text as it was transmitted and copied (as some Latter-day Saint scholars theorize) then the presence of anachronisms is not as much a problem, as one could easily explain these anachronisms as the result of scribal interpolations. (This, incidentally, is a recognized phenomenon that appears to have occurred in the transmission of other ancient texts such as the Bible.)

 See:

Translation and Historicity of the Book of Abraham

The Pearl of Great Price: A Verse-by-Verse Commentary

Authoring the Old Testament: Genesis - Deuteronomy (See the author's chapter on the Book of Abraham)

The Jewish Origin of the Book of Abraham