After some quick googling today I was able to get my galaxy note 4 running PS4 remote play using a DS4 connected via bluetooth with no input lag. It was really easy and I wanted to post it all in one place just incase some people were not aware.
Download the apk and install on your device (just install and it works great and has bluetooth ds4 support built in however it is super laggy on input)
So download "Bluetooth Auto Connect" from UniqTec on the play store and open it up after you pair you controller and have it connected then under advanced options hit "connect now". after that it should work flawlessly. (I left all options default on the app)
To connect your controller via bluetooth hold the playstation button and share button at the same time for a few seconds until the LED starts blinking. It should pop up under bluetooth devices on your phone.
I don't know if all of this is safe or whatever but I have been using it and its working awesome.
Edit: The controller seems to not turn off automatically so just hold the playstation button down until it does (takes about 10 seconds)
Edit2: apk download page
