We know Legion raid bosses can drop legendary items and the chance remains in different difficulties. So you can go in Raid Finder, Normal, Heroic and Mythic to kill the same boss(es) 4 times for loot and you have 4 chances to get a legendary.
My question is different, though. Is it possible to get a legendary item from a raid boss you have already killed this week on that difficulty? You can use another bonus roll on that boss, but you can't loot normal items from it and legendary items are special personal loot, so this is somewhat tricky.
I've heard rumors about this being possible, but haven't seen this, yet. We even cleared Heroic Emerald Nightmare a couple of times when recent server lags made it hard to go Mythic, so my people were sure to get another shot at a legendary.
PS: This is only about raid bosses. Dungeon bosses grant loot every time you queue for them, so they always have their legendary drop chance.
Best Answer
You won't get a legendary from a boss that you've already killed.
There are basically two loot tables in play when looting a (raid)boss.
Whenever you kill a boss you'll always have acces to the bonus loot table regardless of the loot system.
The boss loot table works a bit different if you use bonus rolls or are using the personal loot system. If you don't win anything with either a roll or the persoloot RNG you'll simply get gold.
Now if you have already killed a boss you are locked out both loot tables. This means that you won't get any gold artifact power or legendaries. Since a bonus roll will always roll for the Boss loot table (with gold as a backup) it's not possible to get artifact power, BoS, runes or a legendary if you've already killed a boss.