I'm fairly sure in this case that it means you do not have any more messages to read, despite the arrow blinking. When you have more messages than will fit on your screen, then you get a red scroll bar on the right hand side which you can click and drag to move. I've highlighted it in the screenshot below.
This shows my messages scrolled to the very bottom of what I have received. When I hit the bottom, the arrow at the top appears letting me know there's more up above. Given the lack of scrollbar in your case, you likely just don't have any more and it's blinking because that's all there is on the screen.
I'd like to note that oddly enough, despite the mouse scrollwheel working elsewhere in the UI (like the Journal and Codex), it does not in this case, and requires you to click and drag.