You don't provide details about your furnace but I guess you could measure the oil flow (probably light oil = diesel) with a flow meter like the following:
http://www.conrad.ch/ce/de/product/150392/?DURCHFLUSSM-ANSCHL-6-MM-FCH-M-POM-LCSorry, the description is in german but all documents are in english, I use 3 of these with Arduino. You get the flow very precisely (1 tick/0.5 ml) and you could lift that with a little inlet. I don't know if you have a possibility to get the burner state (some contact should be available) but with the flow meter you get the time when it's consuming oil which is an approximation of the burning time.