Unfortunately official iOS to date (v10.2.1) doesn't support ".gif" file format in Apple's build-in "Photos App" on iPhones at this moment of time. You can however still store in the app and can normally send as digital messages such as in "Mail" or "Messages" Apps. Note that iOS can enable .gif file to play in "Mail" and "Messages" App, hence in the process of sending yourself .gif file in email or text message you will be able to view or play the content of .gif files. The fastest way to view .gif file in "Photos" App is in the steps of emailing a photo - only 2 clicks away from .gif file.
Step 1: Select the .gif file in Photos App (You will see the first still image of .gif as preview)
Step 2: Press
in the process of sending the file in Messages or Mail or other.
Step 3: Select
(
won't play .gif until you send yourself and receive to view in animation)
Step 4: VOILA! You will see .gif file is being played.
Hope it helps.