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 that way (it can't use WiFi, or no data on it) then I would really suggest you ask someone you know who has a computer to assist. It will take less than 10 minutes to move the info from the old phone, via USB cord, to an empty folder on the computer and then move it over to the new device.