Deaths per mile is a good metric in that it is the same for everybody, so to speak, but this is also a weakness. Some people fly far further than they drive or _would_ drive, so for them we should look at per-journey metrics. This must be calculated individually because we all have different typical journeys, but it produces a more meaningful number. For example, any given day that I drive, I drive around 10 miles. When I fly, I usually fly 2600 miles. Over billion days on which I drive, I die 57.5 times, and over a billion flying days I die 156 times - so for me, I am ~3 times as likely to die in transit on a day I fly as on a day I drive. _That's_ what I think about when I file onto the plane. I'm not comparing my odds of death to the hypothetical equivalent drive, in part because I wouldn't drive that 2600 miles so it's an apples to oranges comparison. I'm comparing my odds of death today to my odds of death yesterday and my odds of death tomorrow!
I really doubt if you dug into the flying statistics that all those miles are created equal. Apparently only 16% of air crashes happen during the cruise portion of a flight[1]. You probably need to consider the chance of crashing on a per-flight rather than per-mile basis (as 84% of accidents happen in the takeoff and landing phases, which are approximately the same length for all flights). A long haul flight (which 2600 miles would be) would therefore appear to be more dangerous than it actually is.
The same page gives the odds of dying in a single airplane flight as 1 in 29.4 million. The odds of dying per mile driven are approximately 1 in 174 million. On that basis, your 10 mile journey has a risk of death of approximately 1 in 17.4 million - death is 1.7x more likely.
There's probably a bunch of other ways to interpret the statistics - car miles aren't created equally either, there's a difference between long haul and short haul flight fatality statistics, there's a big difference based on where the airline operates. It's (like all things in life) not very clear cut.
You bring some good information into this, which also gets more to the point I was trying to make, specific math aside - though I am comforted your math shows my flights are probably safer! Given that neither airplane journeys & miles nor automobile journeys & miles are created equally, per-mile statistics aren't particularly meaningful to an individual traveler.
First those 2600 miles are not absolutely safe, so it is a higher risk than an average trip.
And if you qualify the airline deaths based on journey type then you also need to qualify the car trip by journey type. As he is presumably sober, not tired, using a seat belt, not speeding 30+ MPH over speed limit etc his risks of dying over 10 miles is less than half that of the average 10 miles driven.
So, his risk of death per trip is actually higher when flying.