Do so by tapping the grey gear icon on one of your Home screens (it might also be in a folder named "Utilities").;
,,, It should turn grey, signifying that your new photos won't be uploaded to iCloud and then shared across your devices.
Open your iPhone's Settings.
Scroll to the fourth group of options and select iCloud.

,
Select Photos.

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Slide the My Photo Stream switch left to the "Off" position.
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