I had a hard time connecting my Gear S3 to my Note 5, sad to say, it took 2 days to finally configure and connect my two Samsung devices.
I sent a technical support email to Samsung and there solution is listed below:
To connect your mobile phone with the Gear device.
Please know that in order to connect the two, if the Bluetooth connection is a stable one, the devices are found for
pairing and the two are compatible, then you need to make sure that you have Samsung Gear installed on your device, from
Samsung Galaxy Apps > Search > Samsung Gear > Install.
Also, to do this, you have to be Signed In to your Samsung Account from
Settings > Accounts > Add Account > Samsung Account > Sign In.
Should you've taken all these steps and the situation persists, then please reset the Samsung Gear application from
Settings > Applications > Application manager > Samsung Gear > Force Stop > Storage > Clear Cache, Clear Data,
and follow the steps below to reset the Gear connection settings and try again, as it should fix any potential internal software issues.
1. Reset Gear
Gear [Settings] > [Gear info] > [Reset Gear]
2. Reset Bluetooth pairing
On your device, go to [Settings] > [Bluetooth], and tap the cogwheel of the device added
3. Pair Gear
On your device, go to [Settings] > [Bluetooth] > [Scan], and select the Gear you searched for.
If the devices still fail to connect, I recommend you to contact my colleagues in the technical department at http://www.samsung.com/support as they should be able to assist you in mending any hardware issues that prevent the connection from being realized, or check if the devices are compatible.
If you encounter any other unexpected situation and have more questions, please do not hesitate to contact us and our support team will assist you with all the necessary information.
Also, If you visit the Content & Services customer support website, http://help.content.samsung.
For more help you may visit Samsung website : https://help.content.samsung.