If you only see dots when another player is chatting, it likely means you have not unlocked the chat feature with that player. To unlock chat, you or they will have to offer each other Candles to increase your Friendship level until you unlock the chat feature with that friend.
Alternatively, if you are playing on an iOS device, it is possible Public Chat has been disabled on your device. If this is the case, you can check and reenable it by navigating to the Sky app settings in the device settings of your device. When you get there, it will look like the image below.
This option is not currently available on Android devices.