In LiveTraffic‘s Settings you need to enable the output channel ForeFlight. Usually, your own position and the planes created through tracking data ("traffic") will appear soon in ForeFlight.
Finde them in Settings > Output Channels > ForeFlight:
Send user's position
Broadcasts user's plane position (GPS) and attitude (ATT) data in ForeFlight format (if ForeFlight output channel is enabled, too).
Broadcasts traffic data (TRAFFIC), i.e. position information for all the live traffic planes shown (if ForeFlight output channel is enabled, too).
Send traffic every
Repeat interval for traffic broadcasts
In ForeFlight, make sure the device "LiveTraffic", which appears as soon as the app receives the first broadcast from LiveTraffic, is enabled. This is usually the case and it should also not disable itself, but just to be sure:
To see other traffic than only the user's plane also enable the layer called "Traffic".
If you are a developer you could actually make use of the broadcasted data for other purposes than ForeFlight, see here for more information.