Don't buy anything but espresso and ice, Chaos mode's big earner. Buying more ingredients will just increase the complexity of the drinks without adding that much of a reward.
Keep making basic drinks and try to get the clients excited by milking the barista as much as possible so you can sell breast milk, the second highest value ingredient. During idle time, pet her. If she's getting close to overfilling, buy happiness (turns out money can really buy happiness) or increase her capacity.
Once you have ice, it's only a matter of time before you have the money needed to reach max size. Milky mode speeds the game up but you may need to buy calming tea to give yourself a little more of a buffer.
In Ultra-chaos mode you will want to always buy coffee back right after you pour it or you'll only get all milk orders and dig yourself a hole you won't be coming back out of again. Overwrite regular milk orders with breast milk and if you can't, giving out an empty cup is worth the loss of happiness if you can count your earnings on one hand. Some patience will be required and you'll want to keep petting the barista while waiting for her milk to refill. Buy the most valuable toppings and get one or two pourable ingredients so you don't need to re-buy coffee each time.