I'm very familiar with how Amazon feed API works and exactly know how to add variation to your product by feed API.
I've worked for e-commerce company for 4+ years and my main job was managing third party vendor (Amazon, eBay, Walmart, Rakten, and Jet) feed API (feed creation/upload/handling feed response to interact with internal database).
Here I suggest very simple and clear way.
1. create a parent and child products with Parentage and Variationtheme tags in Product Feed.
<MessageType>Relationship</MessageType>
<message>
........
<variationdata>
<parentage>parent</parent>
<variationtheme>Flavour</variationtheme>
</variationdata>
</message>
<message>
........
<variationdata>
<parentage>child</parent>
<Variationtheme>Flavour</Variationtheme>
<Flavour>Beeswax</Flavour>
</variationdata>
</message>
.....
2. post request to define relationships between the products (Relationships Feed)
<MessageType>Relationship</MessageType>