@UnderhiveGangstar :
Honestly, it's very fuzzy. That's just the way I interpret the rules (probably influenced by how it works in Kill Team), but I wouldn't mind a clarification.
The rules for Lasting injury (p87) read "If an Injury roll results in more than one Out of Action result, a separate roll for each is made on the Lasting Injuries table and each result is applied". So you need a
single Injury roll to result into multiple OoA results for this to apply.
The rules for Injury dice (p71) read "Out of action: The fighter is immediately removed from play". So, if an Injury roll takes a fighter out of action, there is no need to make any more Injury rolls for that fighter as they don't exist anymore.
My understanding is that you make one Injury roll per (wounding, unsaved) hit, and not one big Injury roll per attack. After all, each hit leads to a separate Wound roll and a separate Armour save roll, so there is no reason Injury rolls should work differently.
However, I'll retract my previous statement that hits are resolved sequentially. If it were the case, then Flesh wound from the first hit would change the Wound roll for the second hit, and I don't think it's how it's supposed to work.