Justine Drennan ('The Black-Market Battleground, Foreign Policy October 17, 2014) discusses the contribution of the trade in looted antiquities to ISIL funding (see post above). The actual amounts of money being made from selling antiquities is essentially impossible to estimate. The journalist - noting that Al-Azm and Danti were very hesitant to give any estimates - suggests (though not stating a source) that "looting appears, though, to be not only the second-most profitable source of ISIS income" adding that [non-specified] "others have reported that the group's earnings from antiquities are surely worth millions, helping make the Islamic State the world's richest terror group" (except they are not - here - "terrorists"). As for the distribution networks, Drennan writes:
The Islamic State profits nearly immediately, selling the goods to middlemen who then smuggle them into neighboring countries such as Turkey, Jordan, and Lebanon. But fencing the antiquities takes much longer, and that means that once they leave Syria and Iraq it becomes more difficult to determine their fate. Some middlemen belong to organized crime syndicates that smuggle a range of things -- electronics, people, antiquities -- and have done so since long before the rise of the Islamic State. That traffic, along with the illegal arms flowing in the opposite direction, is a large part of why control of border locales such as Kobani is so strategically important, Danti said. [...] "The material is gradually, incrementally laundered in the world-antiquities market, and it becomes very difficult to establish when, where, who, what, why at that point in time," Danti said.Drennan points out that it is obviously "easier for the international community to intervene once artifacts leave ISIS-controlled areas". She suggests that "concerned observers can try to raise awareness and exert moral pressure on collectors not to buy likely trafficked items". Oh yes, I guess she's not talked much with those collectors and dealers... She mentions attempts to get the UN to ban sales of Syrian artefacts as an extension of the existing one on Iraqi ones. Rick St. Hilaire is also extensively quoted, suggesting that "at least some recently looted items [from Egypt, Iraq, Lebanon, Syria, and Turkey] are making their way to the United States" piggybacking on an increased licit trade.
UPDATE 18th November 2014
For the second biggest claim see the Chasing Aphrodite breakdown:"Danti’s Inference: The Known Unknowns Of ISIS and Antiquities Looting" (Jason Felch November 18, 2014).