I just ran a few tests using a Sherwood Archer unit modified to have uber missile stat (I set 100 but 63 is what took) but only 8 men (my unit setting is 1.25x which made 10 + 1 for the general = 11). The results for gaining XP worked out to the following:

1 bronze chevron: 22 kills
2nd bronze chevron: 28 more kills
3rd bronze chevron: 33 more kills

I did this by letting the archers auto-fire at an incoming group of scottish pikemen. The "2nd bronze chevron" result is from a unit I started at 1 chevron and stopped the fight as soon as it gained 2nd. Likewise with the 3rd chevron result, it represents a unit only gaining 3rd chevron from 2nd - it took 33 kills to do so. I wasn't able to go any higher, as the enemy unit gets to the archers before they kill enough to gain a silver chevron from the 3 bronze level. I'm trying to figure out some way to keep it going...

So looking at those numbers, it appears that 1st chevron requires kills equal to 2x the unit's size, 2nd requires an additional 2.5x unit size, and the 3rd requires an extra 3x unit's size to be gained. To determine kills to get to a given XP, you'd just add up the levels along the way. 1 to 3 would be 2.5+3=5.5x unit size needed in kills. In practicality, though, this probably means that the total unit kills from surviving members must be at least a given multiple of their number. So 10 remaining members of any given unit would need 2+2.5+3=7.5 average kills per man (total) to be 3 bronze level. 7.5 x 10 = 75 total kills between them as a unit. 20 total kills would've been 1 bronze, while 45 would make those 10 men 2 bronze.

If we extrapolate the results I just saw, we could guess that a full chart showing additional kills needed to gain each subsequent level would look like the following:

1 bronze = 2.0x unit size in kills
2 bronze = 2.5x unit size in kills
3 bronze = 3.0x unit size in kills
1 silver = 3.5x unit size in kills
2 silver = 4.0x unit size in kills
3 silver = 4.5x unit size in kills
1 gold = 5.0x unit size in kills
2 gold = 5.5x unit size in kills
3 gold = 6.0x unit size in kills

Total kills needed for each level would then be:

1 bronze = 2.0x unit size in total kills
2 bronze = 4.5x unit size in total kills
3 bronze = 7.5x unit size in total kills
1 silver = 11.0x unit size in total kills
2 silver = 15.0x unit size in total kills
3 silver = 19.5x unit size in total kills
1 gold = 24.5x unit size in total kills
2 gold = 30.0x unit size in total kills
3 gold = 36.0x unit size in total kills

Those numbers also represent the average kills per man. If the extrapolation turns out to be correct, then no wonder it's so difficult to have gold chevron units, as they'd require an average of no less than 24.5 kills per man to hold that status.

Also note that this should all be taken with a grain of salt. I've not as yet confirmed anything for other units or for higher experience levels than 3 bronze, so my speculation may differ substantially from the fact of the matter - I just wanted to post it once I hit a roadblock and noticed how nicely the pattern was shaping up.