How do you paint to make it look old like the paint is coming off?

Spread some wood glue, add crumpled up lots of chips in glue. Paint, then scrape some off. Add a sealer like aquathane low gloss.

Milk Paint is the best way to get the chippy look! You can check out Miss Mustard Seeds line. I've used it several times and it works great! :)

crackled paint finish here are how to videos you can watch then choose https://www.youtube.com/results?search_query=DIY+crackle+painting+furniture

Here’s a dresser I did, products and techniques

https://wiselittleowlfurniture.com/chippy-white-dresser-using-crackle-medium/

You sand it in areas that would naturally chip away (corners/edges/etc).

You can also use a crackling medium to get the crazed paint look showing the undercoat color.... https://www.youtube.com/watch?v=0Yz0ZzbpfFY