Did some research to find out what was needed to rank up as some people had higher combat ranks, yet lower kills that people had claimed on Frontier forums.
After looking into it, I found the ranks are all income based. Which for combat, means bigger is better!
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If you have any concrete data to add to, or contradict, the information I have, feel free to chip in.
Looks about right to my stats.
The combat part makes sense as I've ranked up after killing a succession of larger ships with higher bounties. I've not racked up that many kills in total.