Battle Moveset

A Good Moveset for Typhlosion would have to be this:

Attacks:

Sunny Day
Flamethrower
Hidden Power Electric/Grass OR Toxic
Earthquake

Items Attached:

Petaya Berry

Preferred Nature:

Timid

Strategy Using Typhlosion

This is quite hard to give a pokemon with high special attack and little moves to use that special attack, a moveset. Since the only two special moves it learns apart from Hidden power, are fire type moves and a psychic move(Rest).
Anyways, Sunny day and Flamethrower is an obvious must for this moveset, especially on a fire pokemon like Typhlosion. Its weaknesses include Water, rock and ground type moves. So if you come up against a pokemon such as these types, although you may not, use Hidden Power Grass/Electric to cover the type weakness.
If you don't manage to get either HP on Typhlosion, choose Toxic, simply because it doesn't learn many other moves to prove helpful for this pokemon. Having Earthquake on this moveset may seem slightly stupid, but it doesn't have too bad stats in attack either and knowing how strong Earthquake is, it could possibly deal enough damage on a pokemon that the other moves don't.
Try and boost Typhlosions special attack power and speed with EV's and the correct nature. Although Timid lowers Typhlosions attack, you could pick a nature that decreases one of its defenses instead.
Overall, this Pokemon is kind of pathetic, if only it could still learn the punches, then it could've done some much better damage.

EV Corner:

Max out the EVs in Special Attack & Speed for Typhlosion with any remaining in Special Defense

Strategy Against Typhlosion

Typhlosion's Defenses are highish and above average, but it's Physical is slightly weaker to it's Special so attack with Physical attacks or Rock, Ground or Water type Attacks

Contest Moveset

A good Contest Moveset for Typhlosion would have to be this for the Beauty Contest best with Modest, Mild, Rash or Quiet Nature:

Attacks:

Sunny Day
Flamethrower
Earthquake
Hyper Beam

Items Attached:

Blue Scarf

Strategy Using Typhlosion

If you do the attacks in this following order you should have very few problems; 1st - Sunny day, 2nd - Flamethrower, 3rd - Sunny day, 4th - Flamethrower, 5th - Earthquake/Hyperbeam

Locations in Games

Ruby/Sapphire Trade from Colosseum Colosseum Evolve Quilava Fire Red/Leaf Green Trade from Colosseum

Animé Appearences

Typhlosion has had a few Animé Appearences. First, It was owned by Yoshi from New Bark Town and he used it on his Adventures and to stop Team Rocket stealing Raikou. After that, Mura, Flannery's Grandfather had one and used it in Gym Battles and to fend off Team Rocket Special 3: Raikou! Legend Of Thunder! Episode 291: Gonna Rule The School! Episode 331: The New Gym Leader Flannery! The Hole-Filled Battlefield!