Right-clicking does bring up the flash player context window, even in Flixel. Flixel hs no knowledge that the right mouse is ever pressed, that information is not transmitted to the flash "application". Instead, the Flash player tells the app that it's lost focus (since the user is interacting with a context menu for the player and not the app itself). That's what's causing the Flixel pause screen.
I know this for certain because I sit with my 3.5 year-old daughter and play flash-based games with her all the time. She has small hands so she doesn't always hold the mouse quite right, and occasionally will right-click (or click outside of the player window) on accident. Some flash games handle the interruption better than others, with Flixel's auto-pause being one of the more graceful ways. In some games it'll actually lock it up for a bit and get the context menu stuck waiting for input that isn't wanted on our part.
In short, if your not getting the context menu, it's due to the flash player (perhaps a setting? linux version differs due to the OS?), not the game/engine. To say it's the game's fault would be like blaming a bug in a word processer on the document you loaded into it.
I suggest a test. Go to Kongregate and try right clicking in about 20 different games of different types (but all flash). Be sure you're n the game and not an advertisement. What are the results?