I just received a D5600. I have a Motorola Droid (XT1080) running Android OS. It has BT, WiFI and NFC. I installed the SnapIt was somewhat challenging getting the phone to pair with the camera via Bluetooth. Even more of a challenge having it connect via WiFi. Here are the steps that eventially worked (although the WiFi is still not reliable). Sorry about the lengthy wording, but I think it helps to know details along the way, as the camera is not particularly obvious about what's going on.
First, when the camera is initially turned on, under the SETUP MENU (wrench icon), scroll down to page showing WiFi, with Bluetooth just beneath it. The Bluetooth may be dimmed and selecting it gives the message you describe. Above it, you can select the WiFi to see the sub-menu. I suspect you will see all 3 items (Network settings, Current settings and Reset connection settings) are bright and can be selected. At one point I changed the SSID and password, even turned off the Authentication ("open"). It did not have an effect on the eventual result, and they returned to their factory version later on. So I would leave those alone. But you should note the SSID (e.g. D5600_2035566) and the password (e.g. NIKOND5600) under "Current settings" for later use.
OK, so the 1st thing to do is make sure the Bluetooth is set to "Visible to all nearby devices" and the NFC is set to "Allow date exchange when phone touches another device". I went to my phone's Settings menu (cog symbol) to get to these. For the NFC, I had to select "More ..." to get to the relevant sub-menu with the actual NFC settings. This may be specific to my phone and Android version. I also turned on "NFC Security Reminders" and "Android Beam" so that it is ready to transmit app content via NFC.
I suggest closing and re-starting the SnapBridge app on the phone at this point. It should show a screen with a phone symbol on left and camera on right with a circle connecting them (and the BT symbol in the middle). You now have BT connection and can view or download images no larger than 2Mb (2nd icon from left near top -- with mountains in a frame). But the Remote photography and the Download selected pictures (full size) need the WiFi. Those two features are under the next SnapBridge icon (camera symbol).
For the phone WiFi, turn it on and go to the usual setup menu for choosing the appropriate network (access point). On my phone there is a plus sign "+" at the bottom that is used for adding a network that does not automatically appear. The D5600 apparently does not broadcast its SSID. You enter the SSID (from above), select WPA-WPA2-PSK/AES security method and enter the password, then done/save. Now, go back to your phone and open SnapBridge again. It should go right to the page showing that the camera and phone are paired via BT and ready. Select the little camera icon near the top and from the new menu select either Remote photography or Download selected pictures. It will show a progress bar for "Establishing a connection to the camera". Sometimes this is reasonbly quick (a few seconds). Other times a minute or two. Other times it fails with a failure message. For me, I always got the failure message until I re-booted the phone in SAFE MODE. Apparently this clears some of the Android caches that prevent the special WiFi connection method Nikon uses. I then re-started in normal mode and that got the two things to connect by WiFi. Whew!!
Some other things that may help. First, I set my phone to not automatically connect to any network that it normally sees (i.e. my home internet WiFi router). Second, my phone can be put into SAFE MODE by pressing and holding the power button (usual step to turn phone off) and then pressing and holding the "Power Off" confirmation on the screen. A subsequent re-start will put you back in Normal Mode (there may also be a little icon in the status area that you can select to return to normal).
In sum, it seems that the D5600 needs to connect via NFC before it turns on the BT. Then, the SnapBridge has to be running and connected via BT to get the WiFi to turn on and connect. When the WiFi is on, I can actually see it on my laptop WiFi. There are also little icons on the camera's normal screen for taking photos (the one showing the shutter speed, f/# and ISO in circles). The icons appear at the top, to the left of the "Fn" icon. One is the BT icon, the other is the WiFi antenna symbol.