As has been said, old type flip phones are being phased out. Towers and carriers are stopping support for the older connections, some will not activate the older type phones anymore. There are a handful of current flip phones that will work. They need to say something like "LTE" or "4G" in order to work. Since they are in less demand, they are more expensive. Companies like Jitterbug do over a model or so, but you get their service, often it's cheaper, or you get more minutes going with a different company. You may have luck finding a deal on ebay, but that's about it.
Depends what carrier you want. Verizon is the only national carrier where I am, so I will say I have seen and used a fair bit an LG Exalt LTE, and it's got a decent screen, very similar to the old phones, works the same, seems solid. Something more durable, Kyocera Dura (couple more letters on there depending on the carrier, I think XV is Verizon, might be some other difference in models), don't know much about that one, haven't seen it in person. Alcatel has a model, when I was looking into them for someone, didn't get a very good impression of them by reading reviews.
I used a flip around the ranch until a couple years ago, I was afraid I'd break a smartphone. I always had a smartphone for town, getting a new one every couple or so years, at most $50 total. I've never had one fail, they all still work. You can set them up without a lockscreen, so you don't need to verify your identity. The newest one I currently use was also $50 total. It has a fingerprint reader, touch that while picking up and it's automatically unlocked and ready to go. I get a ~10 wallet style case from Amazon for all of them. Flips closed like a book, covers the screen, has a place for cards/money, protects the screen, you can drop them and not worry much about breaking.
I've shopped BestBuy online, the store is 90 miles away, I have been in there once. I prefer online, I don't live anywhere near a big town, there aren't many phones on display to look at anyway (within 70 miles or so), and they are MUCH cheaper finding deals online (although, sometimes the deals are through Bestbuy/Walmart, etc.).