An ideal partner for Skyteam would be Thai Airways. Thai serves a large number of destinations in Asia and holiday destinations are its main business. For Europe and US alike, it would shift Thailand holiday business and Asia travel in general to Air France and Delta. Both airlines carry a small amount of holiday business at the moment. While Thai offers already many Europe flights, it only has one US flight to LAX. Korean is not an ideal solution for SE Asia, but complements the Asia coverage in the NE corner.
Thai also flies to A&NZ frequently.
For Thai itself, Skyteam would solve the competition issue with Singapore Airlines.