Dragon riding tamed Wolf problem

You closed the NBT data for the wolf and then opened another compound illegally (missing a comma as well as a tag-name for it). You just separate tags at the same depth with commas.

The entity ID comes at the start of the /summon command:

/summon <entity> X Y Z {dataTags}

As well, all tags are case-sensitive; it's id rather than ID. Fixed command for pre-1.9:

/summon EnderDragon ~ ~ ~ {Riding:{id:"Wolf",Owner:"Kimatuy"}}

If you're using 1.9, the Riding tag has been replaced with Passengers, which is a list rather than a compound (allowing multiple passengers at the same depth) as well as reversing the stack order. You'd summon the host first instead of the top-most entity:

/summon Wolf ~ ~ ~ {Owner:"Kimatuy",Passengers:[{id:"EnderDragon"}]}