Quote from kagaroparenting your chatter frame to kgpanel frame would cause it to hide when the panel is hidden. As for a key-binding. The best you could do is make a macro to hide the panel and bing the macro to a key binding. Keybidingins behind the sceen take a bit of work. You also need to remember you also need to adjust the visiblity of the other frames occupying that spot. As for auto hide/show you could add an event list for PLAYER_REGEN_DISABLED/PLAYER_REGEN_ENABLED to figure out when you enter and leave combat.
Thanks -- I did some more messing around - I decided to use the OnClick functionality to provide toggle between "Omen/Recount" and "ChatFrame3". This works nicely (Using ChatFrame3:Hide() and Recount_MainWindow:Show() and OmenBarList:Show(), and vice versa). However, every once in a while ChatFrame3 just seems to reappear on its own. It seems to be related to new information entering that window. Is there some reason WoW calls ChatFrameX:Show() when new text is added to the Chat Frame? Any way to override this behavior or suggestions on how I could prevent it? I am thinking perhaps I track a state variable and call the Hide() or Show() OnUpdate, but I'm not sure if that might be system unfriendly from a performance perspective.