My ex-girlfriend tells me she doesn't want to be tied down, and I respect that but she said the reason was she thinks I'll get jealous when she flirts but I don't know what to do

Ah may I ask why would she be flirting anyway if yous were together?
To me it doesn't sound like she's ready for a relationship she wants to experience new things
I wouldn't bother with her.

Why does it matter what your EX girlfriend wants? She is your EX. She can do whatever she wants with her life. Are you still holding out hope to get back together?

Yes I'm still holding out hoping back together, she told me that is the only reason because she hates being tied down because she likes the fact that she can flirt with other guys when she's single and when were dating she can't, I told her I didn't mind if she talked to other guys as long as she didn't cheat on me but how can I ensure her and get back together

She just has to make up her mind. If she doesn't want to be tied down then that means she doesn't want to be in a relationship. All you can do is move on and maybe one day she will want to be in a relationship with you again.