Since Ra is the one who makes his Blazing Tornado attack (despite him possibly not having line of sight or any of that stuff), does that mean he also gets to Flame Spike after hazards?
Yes. Bear in mind that Flame Spike still originates from Ra, so the character being attacked by the Blazing Tornado may not be an eligible target for the Flame Spike attack (though you of course aren't obligated to target anyone specific with Flame Spike).
In situations like this it is important to remember that Tornado and Living Pyre will hit allies, which with Tachyon or Baron Blade and flame spike can make for some fun exchanges.