I'm using a Verizon Note 3. Stock. Neo Hybrid case. Power + Home taking screenshots no issues. Press and hold for a second. Screen will flash white border and then image saved notification pops up.
Swipe method works fine also and the setting is in the Settings > Motions and Gestures menu. It's not a palm wave....you have to use the entire side of your hand and swipe the screen:
"You can now capture a screenshot by touching the screen with the side of your hand and swiping across from left to right or vice versa." - per Samsung
Stupid gesture....better off using the buttons or you run risk of switching screens or even zooming one if in browser. Typical Samsung worthless gimmick, just like remote play.