Can you buy flip phones without having data on them?

Yes, non smartphones do not require data plans

Hello @Kerrigan1997, and welcome to the AT&T Community Forums!

I am sorry you were unable to find a flip phone at att.com. I can help you with that!

Source: https://www.att.com/cellphones/att/z223-prepaid.html#sku=sku7920249

And here are the GoPhone plans:

 Source: https://www.att.com/shop/wireless/gophone-plans.html 

All postpaid service plans will include data as part of the service package.

As to whether or not you need data, that depends on whether you go with postpaid or prepaid plans. On the postpaid plans, every Mobile Share plan has some data. It's not possible to get a Mobile Share plan without data. As noted above, prepaid does have dataless plans.