Plane Shift: Kaladesh has the Aetherborn race. At the DM's option, they can gain access to ability called Drain Life, a natural attack that deals 1d6 necrotic damage and heals the an amount of HP equal to the damage dealt.
Can the gifted aetherborn's "natural attack" be used with a monk's Flurry of Blows to deal and heal multiple d6 in single round of combat?
Plane Shift: Kaladesh is quite different to other materials published by Wizards of the Coast. It doesn't seem to follow the conventions of other source materials. A clear definition of the Drain Life ability is not provided.
For reference the text of the relevant ability is shown below:
At the DM’s option, an aetherborn character can research methods of achieving this dark “gift.” ... An aetherborn with this gift gains the Drain Life ability: a natural attack that deals 1d6 necrotic damage and restores the same number of hit points to the aetherborn.
Notably no mention is made of what kind of action or range this attack has. Also Natural Attack is not a special term in 5e, so we will have to assume it is equivalent to a natural weapon. Otherwise, it is an action and the answer is definitely no.
The monk's Flurry of Blows ki ability states:
Immediately after you take the Attack action on your turn, you can spend 1 ki point to make two unarmed strikes as a bonus action.
These are specifically unarmed strikes, not natural weapon attacks, as Jeremy Crawford confirmed here. As such, your natural weapons (attack) cannot be used with Flurry of Blows.
The ability as shown in the Plane Shift: Kaladesh document is not worded in the standard Fifth Edition parlance, so some things are difficult to determine. It is only described as:
a natural attack that deals 1d6 necrotic damage and restores the same number of hit points to the Aetherborn.
No mention is made if this is a ranged weapon attack, a spell attack, a melee weapon attack or similar. This is not normal for an ability description. However, we can surmise from the fact that no words such as, "whenever an Aetherborn hits with a _________ attack, it may use its Drain Life ability", that the ability is in itself an attack. Thus its effects cannot be combined with flurry of blows, a dagger attack, an arrow attack or any other type of an attack. However, as worded, it is likely that if the Aetherborn is say, a fighter with the Extra Attack feature, that this ability could be used in place of one or both attacks, since it is described as an "attack" and not an "action".
Other races with natural weapons have text like this:
Tabaxi:
In addition, your claws are natural weapons, which you can use to make unarmed strikes. If you hit with them, you deal slashing damage equal to 1d4 + your Strength modifier, instead of the bludgeoning damage normal for an unarmed strike.
Lizardfolk:
Your fanged maw is a natural weapon, which you can use to make unarmed strikes. If you hit with it, you deal piercing damage equal to 1d6 + your Strength modifier, instead of the bludgeoning damage normal for an unarmed strike.
Minotaur:
Your horns are natural melee weapons, which you can use to make unarmed strikes. If you hit with them, you deal piercing damage equal to 1d6 + your Strength modifier, instead of the bludgeoning damage normal for an unarmed strike.
In all cases, the natural weapons of a PC race in 5e are used to make unarmed strikes, and deal an amount of text of a damage type described in the description. From this, we can conclude that the intention of the Aetherborn's Drain Life ability is also a natural weapon that can be used to make unarmed strikes, dealing 1d6+Strength necrotic damage instead of the normal bludgeoning damage for an unarmed strike.
