Distance between species
Unless someone has already done the work to determine genetic distance between the two species you're interested in, unfortunately the answer is "no, there is no such database".  If representative members of the two species have had their DNA fully sequenced, any of the relevant metrics (e.g., those described in Wikipedia https://en.wikipedia.org/wiki/Genetic_distance) can be used to calculate a value for the genetic distance.  But it's important to keep in mind that "genetic distance" is a pretty vague notion when talking about different species.  There are all sorts of epigenetic factors and gene rearrangements that can play important roles in determining the developmental and phenotypic differences between species; and those factors won't show up in most methods for calculating genetic distance.