If my recipe calls for white rum and I only have Jamaican rum can I still use the same measurements?
It really depends on the recipe. Dark rum tends to have a more complex flavor, heavy on molasses. As long as you like that and feel it will go well with the rest of the recipe, it is fine. It isn't going to make any substantial chemical difference in a way that will affect the outcome, so base your decision completely on flavor and color.
It is certainly a valid substitution (that is it won't alter the chemistry of your recipe) but it may slightly alter (for better or worse) the flavor of the finished product.
You might also be wary of a the many varieties of "Spiced Rum" that may significantly change the flavor profile of your dish. For instance, in my rum cake I prefer to use Sailor Jerry's Spiced Rum over the recommended white rum.
(your mileage may vary)