Q: How do I import pictures on my Iphone 5S from pictures to "My photo stream"?

The easiest thing to do is to add them to a shared stream and invite yourself as a subscriber (see http://help.apple.com/icloud/#/mmc0cd7e35).  Otherwise you would have to:

• Open the photos one at a time and take a screenshot.  This will add a new low resolution copy of the photo to the camera roll, which will then upload to your photo stream; or
• Email the photos a few at a time to yourself, then save the attached photos to your camera roll.  This will add a copy of the photo at full resolution to your camera roll and upload to photo stream