There isn’t a way to do it with just three keys without using modifiers. Although Gully has a good point about using the Context menu items, I like keyboard shortcuts for the Flip commands.I use F2, F3, and F4 for flipping components and Shift-F2, Shift-F3, and Shift-F4 when I want to flip multiple entities. (It’s the same Flip along commands for flipping loose geometry and multiple components. I don’t have any use groups so I haven’t setup shortcuts for them but if I were going to do that, I would use Ctrl-F2 and so on.
Since these keys are on the opposite end of the keyboard and I can hit them with just my left hand, I don’t need to remove my hand from the mouse to use them.