OK what you wrote is kind of confusing but I am going to take a stab at it. If I am getting this, you have an old phone, flip phone, that you want to get info off of and put on the new phone? Well an old phone won't have a lot of things that you can get. Mostly contacts, photos, etc. You can't get all the memory off of it.
The fastest and best we is actually a computer connection, but you said you don't own one. Connecting to another Android device is pretty much a pain and usually doesn't work well. If the old phone has WiFi ability (some do/some don't) you can upload the info you have on it to a cloud or google account, or even email it to yourself, and then download said info to the new device. If you can't gain access to the phone...