It will be tough to pick a single, or even a few, favorite(s). Fire type Pokemon are one of, if not my absolute, favorite type(s). Expect a long list, though I'll do my best to keep it short as possible.
Vulpix/Ninetails -- To keep this list short as possible, I'm grouping these two together. With Will-O-Wisp and Hex, these two can really do great in battle. Not to mention, their designs. Vulpix. Is. Adorable. Then it evolves into Nintails, which is elegant and beautiful. And based on a kitsune, which is possibly my favorite being of Japanese lore.
Growlithe/Arcanine -- Again, grouping these two together to keep the list short as possible. Like with Vukpix, Growlithe is just one of the cutest things. Then it evolves into the big, cool tiger-dog thing, Arcanine! I think these favorites are mostly because of design.
Typhlosion -- Nostalgic reasons for this guy. He was my first starter Pokemon in SS. Then my sister stole my game and deleted my saved file to make her own. I flipped out on her, because I loved my Typhlosion. Its design, its stats, its moves...this is just a pretty great Pokemon in general.
Charizard/Mega Charizard X -- My Kanto starter of choice when I played X version the first time, and my second favorite starter Pokemon of all time (behind Serperior). Its design is awesome, it's good in battle, and its X version Mega form is finally a Dragon type!
Infernape -- Went through Alpha Sapphire with one, and he never lost a fight. Speedy, with power in both the Attack and Special Attack department...he can turn even a 40 base damage move like Rock Smash into a dangerous move in battle. There are many Fire/Fighting starter Pokemon out there, and even though this guy wasn't the first, he'll always be my favorite of that particular typing, as well as one of my favorite Fire types.
Talonflame -- Cool design, good Abilities, great stats, awesome performance in battle...this Fire type Pokemon has it all! My Talonflame is one of my most treasured Pokemon.
Pyroar -- It's okay in battle, but the main reason is makes this list is that it's a lion. That's it. It's a lion.
Houndoom/Mega Houndoom -- I love Houndoom's design, even if it's not the strongest of the Fire types I've used in battle. It's not really weak, but there are better choices. I love it anyway, and Mega Houndoom's design really bumped this guy up onto my list of favorite Fire types.
Primal Groudon -- It's a legendary Pokemon, it's powerful, and it looks cool.
Chandelure -- I love it's design (Purple fire with the black coloring? So great!) and the fact that it can learn Energy Ball for use in battle. Energy Ball can be a life saver.
Volcarona -- Nostalgic reasons. I had one on my White version team (raised it from an Egg, which is the main reason it made it onto my team) and it performed pretty well in battle. Its design is also pretty neat.
Reshiram -- Many reasons for this one being a favorite. It's a legendary, it's Fire/Dragon (which is one of my favorite type combos), it's good in battle, and it looks awesome. Also... *cough cough* it's generally seen as N's Pokemon, and I love N *cough*