electronic flashers are what usually create the fast flashing, its the built in "bulb failure indication". You need a flasher that does not have this "feature", or a variable load THERMAL flasher. Thermal flasher are the silver colored (usually) aluminum cased flashers... electronic flashers are in plastic cases.

Variable load thermal flashers are about $2-$3 from an auto parts store... you'll also need 2 short wire leads with quick disconnect terminals, male on one end and female on the other... the male ends will plug into the cars flasher socket and the female ends connect to the flasher. With a thermal flasher it does not matter which terminal connects to what, it works either way. You need the leads because a thermal flasher will not fit into the stock flasher socket.

The stock flasher socket should have 3 terminals (my 94 accord does, not sure if a 03 uses the same set-up). One terminal is powered all the time... one is a ground and one is for the "output" of the flasher. Find your constant 12 volts, that will go into the flasher, and find the ground... then you'll know which one is for the output of the flasher. A test light makes this easy.