LE Archangels SP? What is important about the free action part of it if using hypersonic speed. I don't understand. Does that mean he can't use BCF with HSS?

Yes, yes it does.

HSS allows a close combat or ranged combat attack as a free action during movement. Because of that, you cannot use powers which require a close combat action, or activate from a close combat action, while also using HSS. BCF activates when you give the character a close combat action so it does not normally interact with HSS's close combat attack (it needs the close combat action, not just the close combat attack.) Archangel's Razor Wings allow him to be given a close combat action (not just a close combat attack) while using HSS. The close combat action can activate BCF so the special power allows him to use BCF together with HSS.

It's amazing how often the SPs that allow normally incompatible power to be used together highlight how many people were using them together regardless of the rules. I know someone tries every week due to how close the wording is in the rules.

It's really important to remember that:
Power action > close/ranged combat action > close/ranged combat attack

Sorry, I meant can in my first post. Going on my second day with no

A Close Combat Attack is different than a Close Combat Action. HSS usually grants a Close Combat Attack; BFC requires a Close Combat Action to activate. That's why you can't use any of the normal Powers with HSS (discounting Super Strength). This Special Power is similar to the SP Black Adam (BB 055a) has:
EDIT:
Exactly. I mean, don't people realize that we've been complaining about the lack of HSS/BCF compatibility since at least the old mail away Icons Prof. Zoom?