Edit: With Kotlin 1.1 and Kapt3 it works slightly different:
in your project build.gradle:
buildscript {
   ext {
       ...
       plugin_version = "2.3.1"
       kotlin_version = "1.1.2-3"
       ...
   }
   ...
   dependencies {
       classpath "org.jetbrains.kotlin:kotlin-gradle-plugin:$kotlin_version"
       classpath "com.android.tools.build:gradle:$plugin_version"
       ...
   }
}
and in your app build.gradle:
    apply plugin: "kotlin-android"
    apply plugin: "kotlin-kapt"
    ...
    android {
      ...
      dataBinding {
            enabled = true
        }
      ...
    }
    dependencies {
       ...
       kapt "com.android.databinding:compiler:$plugin_version"
       ...
    }
It's really important that the databinding compiler version and the plugin version are identical.
Also note that with kapt3, you shouldn't use the generateStubs flag anymore.
Old Answer
Having the Android Studio plugin enabled isn't enough, you also need to adjust your gradle files a little bit (add and apply the kotlin-gradle-plugin)
Here are excerpts of my gradle files with working Java and Kotlin Databinding
In your project build.gradle:
buildscript {
...
 dependencies {
   classpath "org.jetbrains.kotlin:kotlin-gradle-plugin:1.0.5"
   classpath 'com.android.tools.build:gradle:2.2.3'
   ...
 }
}
and in your app build.gradle:
apply plugin: "kotlin-android"
...
android {
  ...
  dataBinding {
        enabled = true
    }
  ...
}
kapt {
    generateStubs = true
}
dependencies {
   ...
   kapt "com.android.databinding:compiler:2.2.0"
   ...
}
(I'm using a newer version of the databinding compiler here, you probably should do this as well)