How am I supposed to win with a Rot Victory, knowing that the only way to earn Rot points is with cards, but the King gains Rot points every turn.
So how can I have more Rot points than him?
Cards are not the only way to gain Rot. Per the wiki, the other ways to gain Rot are:
First, it's worth noting that the King gains Rot every night, i.e. every other turn.
Rot victories are the most unreliable victory in Armello. Sometimes even a setup designed for a Rot victory will need to abandon it and go for something else (usually prestige). Other times you will get lucky, end up with plenty of Rot, and go for a rot victory from there.
Suiciding into Banes is often a bad idea. It's an inefficient use of turns since you have to return to clan grounds and you lose prestige. There are exceptions- if you're going to die at dawn anyway or sometimes for getting that 5th point (and potentially the 6th in the same battle if you kill each other). Generally though, if your strategy involves killing yourself more than once to gain Rot, you should be going for another victory type.
If you want lots of rot, you want to be drawing as many cards, (ideally spells which have a far better chance of causing rot) as possible. This means having high wits, using every card you can, and burning the rest whether it helps you or not.
Heroes that are particularly suited for a Rot victory are: