The corny/funny line: corny is borrowed humor - it exists independent of her and she's heard it. Funny is generated humor - it comes from your day, her takes, or the conversation itself. Everything below is built to be the second kind, or to show you the shape of it.
Observational (funny first, flirty by implication)
The flirty part isn't in the words - it's in the fact that she's the one you wanted to tell. That's why these work without a single compliment.
Playful confidence
The compliment inside a joke
This is the strongest pattern there is: the joke gives her something to play with, and the compliment rides in without demanding a response. Compare that to a bare "you're amazing", which is a verdict she has to accept gracefully.
Bad vs. better
Why it works: the pun could be sent to anyone (and has been). The second one is a reaction to her specifically - which makes it both funnier and more flirtatious.
Keep the laugh going
When she replies with "lmaoo stop" - don't stop, but don't repeat the trick either. Switch lanes: follow the joke with a real question or a callback to something she said before. Humor opens the door; curiosity is what walks through it. If the thread's been quiet, revive it first: how to restart a dead conversation.
Generated humor, literally
Paste your chat with her, pick the funny tone, and get 10 texts built from what's actually in the thread - the definition of not-corny.
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Specific observation plus playful confidence: "Saw someone walking a cat on a leash and it had more main character energy than both of us combined. Almost." It's funny on its own and flirty because you thought to send it to her.
Corny is borrowed humor - puns and lines that exist independent of her. Funny is generated humor - observations about your day, her takes, or the conversation itself. If the joke would work in anyone's chat, it's corny; if it only works in yours, it's funny.
Usually both, in that order. Humor is participation - it gives her something to play with - while a compliment is a verdict she has to accept gracefully. The strongest texts hide a small compliment inside a joke.
Yes - paste the chat (or a screenshot) and choose the funny tone. It builds jokes from what's actually in the thread, which is exactly what separates funny from corny.