Unless the kill is already perfectly secured, and this is agreed upon by all parties,
or
they are saving their cds for the end of the teamfight to pick up last-hits rather than help,
or
they flash to get the kill before you (when it's clear you would have gotten it anyway),
there is no good reason to be fussing about "kill steals." This is a team game. Your support sets up the engage; you deal damage, they keep you safe, and the person dies. One of you gets kill gold, the other gets an assist. That's a good thing.
If Riot put your idea into practice, it'd make it almost impossible to strategically funnel gold onto the team's carries (and I don't just mean the adc). It would also make it rough to set up a kill for a struggling teammate to get them back in the game, because they might not be able to do enough damage to "earn" the kill.
Also, what about healing? Are you talking about who's done the most damage since the enemy died? Since they last gained health from something other than base mana regen? A specific numerical time frame? For example, suppose your team's top lane is a Lissandra aganst an Aatrox. Lissandra has been poking him down in lane and he's been sustaining it back. Say her damage, in total, equates to 1200. When Aatrox is at 700 health, he backs off a bit, takes krugs to get up to 800-900, and teleports bot lane to gank you. Your support deals 300 damage, and you deal the remaining 600. Who gets the kill credit and why?
EDIT: Why the hell are you playing Garen ADC?