You could link to the game. Riot has given you the ability to do so for a reason. No one wants to manually hunt down one game from however many number of days ago in order to do you a favor. As long as you don't single someone out and talk about them, it shouldn't be against the rules.
Your KDA is only important relative to your team's kills. It's less your KDA and more your kill participation. It's the reason supports can get frequent S ranks for having a bunch of assists, but virtually no kills. Deaths are also a massive reduction for rank; you'd have a better chance of getting an S if you had, say, 2 deaths and 15 kills (most likely). Having no deaths is also a massive bonus to your rank.
How much CS did you have? How many wards did you place? Did you buy any pink wards? How many towers did you kill? How much damage did you deal relative to everyone else? All of these are important questions to consider when asking about your rank at the end of a game.
EDIT: Also, the game length probably decreased your rank as well; the longer a game goes on, the more difficult it is to get an S rank.