Do you mean the feature labels?
To change the orientation of labels go right-click on your layer and select Properties then the Labels tab. There is a button Placement Properties:
The parallel or curved options should make the labels match the stream directions.
Check out these results when flipping features and text:
As Xander says as soon as you flip text you end up with a mirror image that does not make much sense. The flip both example is the same as rotating text 180 degrees:
Generally, text that is upside-down (at any angle) becomes hard to read. Mirrored text is even harder to read.