Anon: 'Blood Money: How Isis makes up to €4.5m a day' Irish Examiner Saturday, November 22, 2014. This is quite a detailed article, and the bit about antiquities is right at the end (but it also contains the controversial "second biggest source of revenue" quote).
So how can ISIS, cut off from the rest of the world by financial and trade sanctions, and under daily aerial and land bombardment by some of the richest countries in the world, afford to maintain a well-armed military and pay other bills? Interviews with Iraqi, Kurdish, European, Syrian and American government officials, analysts and intelligence agents sketch a portrait of ISIS’s robust, sprawling, and efficient financial operation. [...] Its currencies of choice - cash, crude oil and contraband - allow it to operate outside of legitimate banking channels. [...] The ISIS economy and its fighters predominantly rely on the production and sale of seized energy assets - Iraq has the fifth-largest proven crude oil reserves in the world. ISIS also depends on the steady income it extracts from private donors, the heavy taxation and extortion it levies on its captive population, the seizure of bank accounts and private assets in the lands it occupies, ransoms from kidnappings and the plundering of antiquities excavated from ancient palaces and archaeological sites.[...] Ancient objects may be the most lucrative things to sell, but ISIS is not picky; it is also happy to sell stolen wheat, barley, rice, livestock - even people.The smuggling of various commodities seems to be a fundamental part of the system
Turkey’s southern corridor, Iraq’s northwestern corridor and Syria’s northeastern corridor are key weak spots, well away from the prying eyes of outside investigators.[...] ISIS doesn’t “depend principally on moving money across international borders,[...] but obtains the vast majority of its revenues from local criminal and terrorist activities.” This presents a formidable obstacle for the US Treasury, which is accustomed to pursuing its enemies by pressuring established banks to expose their criminal clients. ISIS’s use of middlemen across the Middle East to smuggle cash in and out of its territory, in addition to employing decades-old smugglers’ routes, makes the group especially hard to track.[...] Secret smuggling routes are often passed on by families from generation to generation, and they were well-secured during the lean years of economic sanctions imposed by the West during Saddam Hussein’s dictatorship in Iraq. Border guards were in on the baksheesh system entrenched in the culture. They would turn a blind eye when cash in suitcases or trucks containing oil or goods passed through their checkpoints. Many smugglers who traded Saddam’s oil across Iraq’s borders to Kuwait, Iran and Turkey are now working the same routes between ISIS-held Iraq and the outside world.Basically those antiquities dealers who say they see no "new" flow of antiquities along those smuggling routes are confirming this, the antiquities being smuggled today are being smuggled through the same channels - and most likely through the same people - as they were a decade or more ago.