A feature included with noble intentions, but frequently abused.

If the votekick requires too few votes, it'll be easy to to get rid of cheaters, but good players will also get kicked easily

If the votekick requires too many votes, then you'll never get rid of cheaters. Only yesterday I had one cheater in my game. It was obvious that he was cheating. A votekick was initiated but it failed due to insufficient votes. The people in the same team as the cheater obviously didn't vote against him because it's better to have a cheater in the same team as you. Your team would win, and you'll perform better. Some others were obviously oblivious to the fact he was cheating. You don't really notice cheaters unless they're killing you.

So what is the best way? I think we should have a votekick system which requires 10 votes, but also have a 'report cheater' feature, whereby Crytek can then monitor the guy and ban him eventually.

Or we could make it such that my score and kills register despite getting kicked. At least we won't lose our 20 kill streak or something.

You can't put a number of votes required to kick a player. What if there was only 19 players on the server and it was set to 10 votes required?
One thing players can do is try to get support for votes by telling the other players why you want to call a kick vote.
If Crytek would even look at these threads it might help but they refuse to acknowledge threads about the vote problem. If the player's name was announced it make them think twice about calling BS votes. The way it's set up now, players see so many votes called they just don't pay them any attention.
The same player can call votes all game long. This can be changed by the server admins by increasing the cool down time.

All DDD and C3CG servers have increased Cool-down times and more votes required.
In Crysis 2, admins could review the logs and see who has been calling the votes and who the votes were called on. This helped us deal with the problem politician or hacker/cheater after-the-fact.

But Crytek refuses to address these problems.