Excellent question. According to this DOE source (scroll down to Oil Consumption by the U.S. Military Abroad, which is not all that we'd want to know), oil use by the military is difficult to calculate, because apparently the DOD doesn't keep very good records, and it depends on whether the oil is purchased in the US and then shipped over to military bases, or directly purchased from an international source.

In 1990 (old estimate, I know), the military abroad used about 500,000 barrels a day, and about 350,000 of them were purchased from US sources, "and hence was presumably counted in U.S. domestic oil consumption". But who knows.

I'll look again if I get a moment later today, but in any case, it doesn't look like there's a simple answer.

Please do follow up on this. My suspicion is that the military does not constitute a fifth sector anywhere near the size of the others, although this is taken as given by many commentors. I may be wrong and would like to know. However, since comments like the one above are thrown around so often, it would make sense to try to document this.
The DOE site that ianqui linked to says that consumption has gone down rapidly from the figures cited for 1990. If held constant, they would account for about 1.75% of US consumption and 2.5% if int'l purchases were included. Since they are now lower the military use must be less than 1.75% of US domestic consumption