参考にしたのはここ https://proandroiddev.com/react-native-bridge-with-kotlin-b2afde2f70b

手順

react-native init kotlin

android/build.gradle

buildscript {
    ext {
        buildToolsVersion = "28.0.3"
        minSdkVersion = 16
        compileSdkVersion = 28
        targetSdkVersion = 28
        supportLibVersion = "28.0.0"
        kotlin_version = '1.3.0'
    }
    repositories {
        google()
        jcenter()
    }
    dependencies {
        classpath 'com.android.tools.build:gradle:3.3.1'
        classpath "org.jetbrains.kotlin:kotlin-gradle-plugin:$kotlin_version"
    }
}

android/app/build.gradle

apply plugin: "kotlin-android"
apply plugin: "kotlin-android-extensions"
...
dependencies {
    implementation "org.jetbrains.kotlin:kotlin-stdlib-jdk7:$kotlin_version"
    implementation fileTree(dir: "libs", include: ["*.jar"])
    implementation "com.android.support:appcompat-v7:${rootProject.ext.supportLibVersion}"
    implementation "com.facebook.react:react-native:+"  // From node_modules
}

ここにハマりどころがあって、 implementation "org.jetbrains.kotlin:kotlin-stdlib-jre7:$kotlin_version" を implementation "org.jetbrains.kotlin:kotlin-stdlib-jdk7:$kotlin_version" にしないとだめ（素人感）

準備編はおしまい