#NO, though RAW it is unclear

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.

##Natural vs Unarmed

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.

NO, though RAW it is unclear

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.

Natural vs Unarmed

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.

#NO, though RAW it is unclear

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.

##Natural vs Unarmed

The monk's Flurry of Blows 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.

#NO, though RAW it is unclear

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.

##Natural vs Unarmed

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.

#NO, though RAW it is unclear

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.

##Natural vs Unarmed

The monk's Flurry of Blows 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.

#NO, though RAW it is unclear

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.

##Natural vs Unarmed

The monk's Flurry of Blows 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.