Spinda designs are based on a mechanic called personality values, or PVs. There are over 4 billion different possible Personality values (4,294,967,295 to be exact). So the chances of having two identical Spinda are extremely low. Even Spinda's HeartGold and SoulSilver Poked entry says there are 4 billion designs. Plus, any of these designs can be shiny, so if you count shines there are over 8.5 billion possible designs. That's more than there are people on Earth! So yes, it is TECHNICALLY possible to have two identical Spinda, but the odds are so low that you can safely say you'll never find this.
"Some of Spinda's Pokédex entries mention the odds of two Spinda having the same spot pattern as less than one in four billion. Since Spinda's spots are based on its personality value (a 32-bit number), a simplistic model would put the odds at 1 in 4,294,967,295." -Bulbapedia