As silverplate is a microscopically thin coating, that's kind of like asking what percentage of your living room wall is paint?
but since you asked....
The thickness of the silver layer varies from country to country, maker to maker. For an example's sake let use the German 90 gramm standard. Forum member Bahner has explained here
viewtopic.php?t=7214that 90 grams of silver are used to plate 24 pieces of flatware. Given that your average table spoon weighs about 50 grams and its coating would be about 3.75 grams, the percentage of silver would be about 7.5% of the entire weight of the piece. The equivalent of 1.6 cents in today's silver market.
Regards, Tom
ps. American plate has a tendency to be thinner, than European.