"Spin rate" as in revolutions per unit time (i.e.: RPM)? Or do you mean the velocity of a point on the surface of the planet as observed by a distant observer?
If a record spins at 45 RPM, any point on that record passes by the needle 45 times per minute. Doesn't matter if the record is 6" in diameter or a mile in diameter. But what DOES matter is the velocity of those points.
As pointed out above, for a given period of revolution, the velocity of a spot on a planet near its pole is very much slower than a spot near its equator. If you have two planets, one 8,000 km in diameter and one 80,000 km in diameter, in order for both to have a revolution period of 24 hours, the velocity of a point on the surface of the larger planet (at its equator) will be very much faster than that of the smaller planet.
I think the term "spin rate" has problems: the definition is ambiguous. If we stick with surface velocity (equatorial, to keep apples with apples) and revolutions per unit time (Earth has 365.25 RPY), then we might eliminate much confusion.