With a gas fire situated in a chimney, heat, smoke and soot can be all but ruled out as any form of threat to the TV. Heat will rise within the chimney, barely heating the back of the wall the TV is mounted on, and carry away with it the majority of smoke and soot.
A standard gas fire in most modern homes will come with a blower fan to push generated heat away from the fire and into the room. A filter will remove smoke and soot, while heat generated by the fire and channeled around the cavity will dissipate as it spreads throughout the wall or be radiated away by the casing.
There is however one other thing to consider - heat and the minimum of smoke and soot that does escape from the fire and travels upwards, coming into contact with your flat panel TV and potentially damaging it.
Luckily, this can all be prevented with a standard mantelpiece. The mantel will buffer the heat, sending it into the room and away from the TV. It's also worth noting that various safety standards ensure that the TV itself is protect from outside influences such as domestic heat and dust in order to continue working without issue.