I have a new iphone, I want to delete my account off my old phone but keep my information on my new iphone.

Yes, it's possible. To do so, start by saving any photo stream photos that you want to keep to your camera roll (unless already there) by opening your my photo stream album, tapping Select, tapping the photos, tap the share icon (box with upward facing arrow), then tapping Save to Camera Roll. If you are syncing notes with iCloud that you want to keep, you'll need to open each of your notes and email them to yourself so you can later copy and paste the text into new notes after deleting the iCloud account. Then go to Settings>iCloud, tap Delete Account, provide the password to turn off Find My iPhone and choose Keep on My iPhone when prompted .