I hadn't tried to add a photo from a phone until you asked this question. It looks like it is very simple. 

At the bottom of your new post it says "Insert images by dragging & dropping, pasting from the clipboard, or by selecting them."

Click on "selecting them" and it will open a dialogue on your phone to select the appropriate folder on your phone where your pictures are stored. Click on the picture you want and it will add it to your story. 

Pro Tip: Make sure your blinking cursor is where you want it before you select your photo. It will add it where you left your cursor.

I use steemit.com's full webpage all the time on my phone without issues.  It should definitely work!