The beginning of the chapter goes over the basic Patriarchal Narrative. After this review, the history of the search of the Patriarchs in history is overviewed. At first, the search for the Patriarchs began as an attempt to confirm their existence, and, therefore, bolster the evidence for Christianity. The Baltimore School attempted to do so by using such data as names with Amorite imperfectives and laws relating to family and shepherding. The Amorite hypothesis, attempting to show a migration from Mesopotamia to Canaan, rose with Albright and fell with Thompson. The Nuzi/Hurrian hypothesis also fell. The social and legal parallels were shown to be rather vague. However, as F&S do not mention, no one has yet disproved the Amorite Impefective parallel (note: most info there is unreliable, but the 20 shekels, covenant formats, and imperfective parallels are sourced right from Kitchen himself), nor the fact 20 shekels was an acceptable slave price in the early second millennium.
F&S then start on their list of telltale anachronisms. Their assuming the Gileadite products of Genesis 37:25 Arabian shows their laziness in research quite well. While there do seem to be too many camels, only widely used for trade purposes during and after the Ramesside period, for the early second millennium, and the presence of Ishmaelites as merchants does seem to be indicative of a first millennium date, it is by no means proof of a date of composition between the 8th and 7th centuries BC. The increase in camel bones at Tell Jemmeh/Yurza in the 7th century only indicates a re-routing of the camel trade through Yurza by the establishment of an Assyrian fortress there, not its beginning. Philistines mentioned at Gerar may only be an updating of the narrative, perhaps for Caphtorites, since Gerar was a 38-acre MB site, but the Philistine references can still be interpreted as evidence for an 8th-7th century Genesis. The mentions of the Arameans are very much indicative of a 1st millennium date, but can still be somewhat plausibly assigned to the Mosaic period. Ammon and Moab have been Israelite enemies since the Judges period and are not indicative of any specific date.
The fact some tribes (Edomites, Temaites, nomadic Sabeans, ect.) were first mentioned in extra-biblical records by the Assyrians in the 8th century BC, does not mean they did not exist before that time. Who else would have bothered to mention them? Edom was, contra Finkelstein, a state ruled by a king a century before they were mentioned by the Assyrians (2 Kings 8:20). Bozrah had great citadels well into the mid 8th century (Amos 1:12). Finkelstein, denying the fact Judah ruled Edom until the reign of Jehoram, cannot use Gen 27:40 as evidence Genesis was compiled after the reign of Jehoram.
Ein Qudeirat was neither Kadesh, nor inhabited primarily in the 7th century. Hazezon Tamar is not Tamar. Also, the statement on page 323 the cities of Jerusalem and Shechem are not mentioned in Genesis makes me wonder precisely what F&S and the editors of TBU have been smoking.
In short, the evidence for a 7th century Genesis exists, but not as much as Finkelstein makes up.