How does the Strange PDA track “kills”

You need to crouch jump to reach the ledge from the tires.

I believe Transall wasn't referring to this area when he mentioned the ramp, as there are no container boxes on which you can stand here — you can only stand on the ones around the central control point.

To answer your title's question, strange flamethrowers only count kills done by that weapon's fire damage. This is either through direct damage (W + M1) or the afterburn. It does NOT count reflects sadly. Taken straight from the TF2 Wiki's strange page:

The following actions do not increase the total kill count:

• Killing an enemy with a compression blast.

Strange - TF2 Wiki

As for kill counts, I have a strange degreaser and flare gun too and my flare gun does have a lot more than the degreaser. My guess is in how I play. I tend to ignite, air blast and follow up with a flare gun shot or the axtinguisher. I reflect a lot also (but those kills don't count). If at range I use the flare gun for ignitions and annoying. Since the afterburn damage on the degreaser is less, then you are less likely to get a kill from that than the other flamethowers. Also if you do the air blast and flare gun, the flare gun's afterburn will override the degreaser's so if you get the kill after that, it's for the flare gun.

I would so love a separate counter on my degreaser for reflect kills, like the sentry kill count on the engy's wrench.