What's a good way to casually ask a girl you're flirting with to hang out?

Try making theoretical plans together. They don't have to be specific plans like, "Let's go out on Thursday at 8:00 p.m. to this event." Instead, identify a mutual interest you both share, and then casually suggest future plans based around that. For example, if you both love cooking, you could say something like, "It would be so fun to go together to the farmer's market, get some fresh veggies, and cook something together one day." Or, if you're both talking about a love of comedy, you could say, "Maybe we could see a comedy show some time together."