Milight uses UDP for direct communication over the local network, which is not a protocol currently supported by SmartThings. There are some people who are trying to hack around and find a way to make it work, but not yet.
At present, Smartthings supports zwave and zigbee ZHA 1.2 devices. Also zigbee ZLL bulbs connected to a Hue bridge.
There’s a bluetooth antenna in the hub, but it is not turned on yet.
In the US, Smartthings supports many third-party integrations through cloud to cloud connections, but these generally require the OAuth protocol which is currently broken for the UK. They are working on getting it fixed, but no specific timeline yet.
Some people have added additional integrations by adding additional hardware devices including their own server pieces, but it does get pretty complicated, and it’s best to just investigate each of those topics individually.
So there are certainly community members looking at a possible Milight integration, but there isn’t one right now, and it isn’t going to be easy.