Word up. As was said earlier, a lot of the messengers ride fixed, but my only contact with other fixed gear riders (other than my roommate) is
Bicycle Kitchen. They're REALLY REALLY awesome guys, and are always down for riding or drinking, but usually both. As for parts, there are places in Encino, and this guy down in Redondo Beach. I don't remember the name of the shop, but it's on PCH. It's in the book. Supposedly, he has TONS of track stuff. PM me if you really want me to find out.
Also,
Velo Pasadena has some track stuff (hubs, cranks, cogs, track bars, stems, even keirin gloves and double sprint straps), as well as some of the most decked out roadie biked you've ever seen (from $10k colnagos to a 50/50 schwinn paramount with a 50th aniv. campy gruppo). Owner used to race track. There's a place down the street, Open Road, where Steve Lubanksi has some
crazy pedals and some really nice old stuff (though it's warehouse style, i.e. you have to look for stuff. He has a Schwinn Paramount track frame hanging in the back. Old Mavic Disc wheels, and he knows a BUTTLOAD about bikes).
Other than that, if you happen to be in the LA area (namely highland park) and see some skinny dork tooling around on a blue GT pursuit bike (you'll know it's mine by the uncomfortable looking geometry), yell, "HI KRIS!" because that's me. Feel free to buy me beer, so long as I can't see through it or count it's alcohol percentage by volume on one hand.