Yes you can flip and mirror images in Adobe Camera Raw. Here's how:
Windows: hold the "Alt" button and click on the Rotate button in the tool bar. One is for "flip horizontal" and one is for "flip vertical".
MAC: hold the "Opt" button and click on the Rotate button in the tool bar. One is for "flip horizontal" and one is for "flip vertical".
Note: This does not work within Photoshop's built-in version of ACR, only in ACR launched from Bridge.
There are a few archived posts that say this is not possible in ACR and those answers are wrong. You can flip images in ACR.
