Update your Amazon Fire Phone to the latest OS first.
Then install the following APPs in this particular order:
Google Services Framework, 4.4.4-1227136 https://goo.gl/W4NbMy
Google Play Services, 10.0.84 (036-13749526) https://goo.gl/r3sUsg
Google Account Manager, 4.4.4-1227136 https://goo.gl/XmnzRB
Google Play Store, 7.2.13.J-all  [PR] 138561921 https://goo.gl/GjymJx
Google Now Launcher on Fire Phone
(I don’t recommend this because in my testing it reduced the battery life by a lot.)
If you want to install the google now launcher on amazon fire phone then you need to install the “Google App” first. Launch the app after install and click through the “Get Started” steps. It is important that you go through the Setup Steps in Google App.
Tip: Turn off the “Ok Google” in Google App Voice Settings because this is a battery drain on your phone.
Once you have the Google App running, go back to the play store and download “Google Now Launcher” After you install it make it your default launcher.
Now you can click and hold anywhere on the screen to set widget or change background wallpaper.