Would signing out of iCloud delete my locally stored photos? I am trying to sign into my iCloud on my iPhone 6 and even with the correct password it is not letting me through but keeps asking with a prompt. I have local photos that I do not want deleted and need to pull off the device. If I were to sign out of my iCloud account will it delete the photos that are stored locally?
iCloud always asks you if it deletes local copies and it only deletes copies it knows are stored online, so you should be safe to remove an account.

If you're worried, make an iCloud and iTunes back up just in case, but signing out only is intended to clear things that came down from the cloud and even then it offers you the option of keeping local copies of data in many classes of data (contacts is the one I see often).