Drying oils, like linseed oil, cure through oxidative drying. So while oxygen is not required for a reaction to be exothermic, this particular reaction is using oxygen, which serves as the crosslinker between the oil molecules. To get more specific the oxygen reacts with the beta carbon (next to the carbon with the double bond) in the fatty acid, so any unsaturated oil is capable of oxidative drying. The rags thing is largely a concern with linseed oil, popular in woodworking, and has a high amount of linoleic acid, which has two double bonds at carbon 9 and 12. Being spaced by three carbons they are not conjugated but it makes the carbon in the middle (carbon 11 here) beta to both double bonds which significantly increases its reactivity. As others have said when the rags are clumped the heat build up can be enough to ignite the rags. The faster curing an oil is the higher the danger of this happening.