The way things are worded in the rules the 3/1 attacker will assing all 3 points of its damage to the 3 toughness blocker as needed for combat damage, then damage step will resolve, triggering The Flame of Keld and thus making the actual damage dealt to the blocked 5(resulting in 2dmg overkill), however because you didn't assign any damage to the player blocking no damage will be done to them.
From Gatherer on The Flame of Keld 4/27/2018: If multiple replacement effects would modify how damage would be dealt, the player being dealt damage (or the controller of the permanent being dealt damage) chooses the order in which to apply those effects. 4/27/2018: If damage dealt by a source you control is being divided or assigned among multiple permanents an opponent controls or among an opponent and one or more permanents they control simultaneously, divide the original amount before adding 2. For example, if you attack with a 5/5 red creature with trample and your opponent blocks with a 2/2 creature, you can assign 2 damage to the blocker and 3 damage to the defending player. These amounts are then modified to 4 and 5, respectively.
Then on MTG rules 510.1c A blocked creature assigns its combat damage to the creatures blocking it. If no creatures are currently blocking it (if, for example, they were destroyed or removed from combat), it assigns no combat damage. If exactly one creature is blocking it, it assigns all its combat damage to that creature. If two or more creatures are blocking it, it assigns its combat damage to those creatures according to the damage assignment order announced for it. This may allow the blocked creature to divide its combat damage. However, it can’t assign combat damage to a creature that’s blocking it unless, when combat damage assignments are complete, each creature that precedes that blocking creature in its order is assigned lethal damage. When checking for assigned lethal damage, take into account damage already marked on the creature and damage from other creatures that’s being assigned during the same combat damage step, but not any abilities or effects that might change the amount of damage that’s actually dealt. An amount of damage that’s greater than a creature’s lethal damage may be assigned to it.
June 6, 2018 9:40 p.m.
since this question has been answered now, please mark it as such.