Flipping an image horizontally or vertically with the stock iOS Photos app is not possible. Pictures can be rotated with the Edit function, however getting a mirror image of the photo requires third party software. Fortunately, there are many free options on the App Store. One versatile example is Adobe Photoshop Express.
To flip a picture you have taken vertically or horizontally, install and open Photoshop Express. Give the app permission to access the Camera Roll, then tap Open from Camera Roll to import the image you wish to modify. The image will load.