Any way to link to the Android notification settings for my app?

I merged the solution of Sergei and Shhp to support all the cases :

    Intent intent = new Intent();
    if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.O) {
        intent.setAction(Settings.ACTION_APP_NOTIFICATION_SETTINGS);
        intent.putExtra(Settings.EXTRA_APP_PACKAGE, context.getPackageName());
    } else if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.LOLLIPOP){
        intent.setAction("android.settings.APP_NOTIFICATION_SETTINGS");
        intent.putExtra("app_package", context.getPackageName());
        intent.putExtra("app_uid", context.getApplicationInfo().uid);
    } else {
        intent.setAction(Settings.ACTION_APPLICATION_DETAILS_SETTINGS);
        intent.addCategory(Intent.CATEGORY_DEFAULT);
        intent.setData(Uri.parse("package:" + context.getPackageName()));
    }
    context.startActivity(intent);

The following will work in Android 5.0 (Lollipop) and above:

Intent intent = new Intent();
intent.setAction("android.settings.APP_NOTIFICATION_SETTINGS");
intent.addFlags(Intent.FLAG_ACTIVITY_NEW_TASK);

//for Android 5-7
intent.putExtra("app_package", getPackageName());
intent.putExtra("app_uid", getApplicationInfo().uid);

// for Android 8 and above
intent.putExtra("android.provider.extra.APP_PACKAGE", getPackageName());

startActivity(intent);

Notes: This is not officially supported in Android 5-7, but it works just fine. It IS officially supported as of Android 8. This code is not backwards compatible with versions of Android before 5.0.

For lazy men this is the kotlin version of @Helix answer:

fun openAppNotificationSettings(context: Context) {
    val intent = Intent().apply {
        when {
            Build.VERSION.SDK_INT >= Build.VERSION_CODES.O -> {
                action = Settings.ACTION_APP_NOTIFICATION_SETTINGS
                putExtra(Settings.EXTRA_APP_PACKAGE, context.packageName)
            }
            Build.VERSION.SDK_INT >= Build.VERSION_CODES.LOLLIPOP -> {
                action = "android.settings.APP_NOTIFICATION_SETTINGS"
                putExtra("app_package", context.packageName)
                putExtra("app_uid", context.applicationInfo.uid)
            }
            else -> {
                action = Settings.ACTION_APPLICATION_DETAILS_SETTINGS
                addCategory(Intent.CATEGORY_DEFAULT)
                data = Uri.parse("package:" + context.packageName)
            }
        }
    }
    context.startActivity(intent)
}

I've appended Channel Notification Settings for Android 8.0 Oreo API 26 or later. There is a solution from Android 4.4, KitKat.

Usage for Channel notification settings:

// PRIMARY_CHANNEL:
goToNotificationSettings(getString(R.string.PRIMARY_CHANNEL), mContext);
// SECONDARY_CHANNEL:
goToNotificationSettings(getString(R.string.SECONDARY_CHANNEL), mContext);

Usage for App notification settings:

goToNotificationSettings(null, mContext);

The method of goToNotificationSettings:

public void goToNotificationSettings(String channel, Context context) {
    Intent intent = new Intent();
    if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.P) {
        intent.addFlags(android.content.Intent.FLAG_ACTIVITY_NEW_TASK);
        if (channel != null) {
            intent.setAction(Settings.ACTION_CHANNEL_NOTIFICATION_SETTINGS);
            intent.putExtra(Settings.EXTRA_CHANNEL_ID, channel);
        } else {
            intent.setAction(Settings.ACTION_APP_NOTIFICATION_SETTINGS);
        }
        intent.putExtra(Settings.EXTRA_APP_PACKAGE, context.getPackageName());
    } else if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.O) {
        if (channel != null) {
            intent.setAction(Settings.ACTION_CHANNEL_NOTIFICATION_SETTINGS);
            intent.putExtra(Settings.EXTRA_CHANNEL_ID, channel);
        } else {
            intent.setAction(Settings.ACTION_APP_NOTIFICATION_SETTINGS);
        }
        intent.putExtra(Settings.EXTRA_APP_PACKAGE, context.getPackageName());
    } else if(Build.VERSION.SDK_INT >= Build.VERSION_CODES.N_MR1) {
        intent.setAction(Settings.ACTION_APP_NOTIFICATION_SETTINGS);
        intent.putExtra(Settings.EXTRA_APP_PACKAGE, context.getPackageName());
    } else if(Build.VERSION.SDK_INT >= Build.VERSION_CODES.LOLLIPOP){
        intent.setAction(Settings.ACTION_APP_NOTIFICATION_SETTINGS);
        intent.putExtra("app_package", context.getPackageName());
        intent.putExtra("app_uid", context.getApplicationInfo().uid);
    } else if (Build.VERSION.SDK_INT == Build.VERSION_CODES.KITKAT) {
        intent.setAction(Settings.ACTION_APPLICATION_DETAILS_SETTINGS);
        intent.addCategory(Intent.CATEGORY_DEFAULT);
        intent.setData(Uri.parse("package:" + context.getPackageName()));
    }
    context.startActivity(intent);
}