Where to get skitty in soul silver?

You can't get Skitty in SoulSilver! Skitty is a Generation III Pokémon and was introduced in Ruby and Sapphire, which came out after SoulSilver.

If you're looking for a similar Pokémon in SoulSilver, you might like Spinda. It's a Normal-type Pokémon and can be found in the Route 35, 36, and 40.