I am not very familiar with baraminology, but I found this:
Major Additive Criteria:
Succesful interspecific hybridization. If members of two different species can successfully hybridize, they share genetic and morphogenetic programs and are, thus, holistically continuous. Although Marsh (see historical context) relied on hybridization as the single method of identifying which species were members of the same baramin, the problems with using hybridization as the exclusive baraminic membership criterion are many. Asexually reproducing species and species known only from fossils are impossible to classify using hybridization. Even among sexual species, failure to hybridize may be due to other causes than discontinuity.
Morpho-molecular similarity. Are the natural and artificially hybridized forms linked by overlapping quantitative measures, by character-state transitions in which all the states are observable in known and otherwise similar organisms, or by a homoplastic distribution (recombination) of redundant character states among similar organism? A statistical measure has been developed called Baraminic Distance (BD). A positive correlation of BD is interpreted as evidence of continuity of two organisms.
Stratomorphic Series. Stratigraphic fossil series connected by clear character-state transitions are evidence of continuity. For example, fossil and modern equids qualify as a monobaramin (see Cavanaugh et al. 2003).
Major Subtractive Criteria:
Scripture claims discontinuity. This should be concluded only after completion of a semantic and contextual study of relevant words and passages. Clear examples are that Scripture claims humans to be an apobaramin and that cetaceans are discontinuous from land mammals (i.e., each created on separate days).
Morpho-molecular dissimilarity. Are the natural and hybridized forms within the group separated from organisms outside the group by gaps that are significantly greater than intra-group differences? A negative correlation of BD is evidence of discontinuity.
Unique synapomorphies. Is the group circumscribed by a set of unique morphologies or molecular sequences? These synapomorphies should lack empirically observed transitions to states in other supposedly related but outside groups.
Lack of fossil intermediates. That is, there is no known fossil ancestral group, and fossils with "ancestral states" or "states transitional to other groups" are unknown. Forms identifiable in Flood sediments were probably distinct from the time of creation. A good example is Archaeopteryx, which likely represents its own unique baramin, distinct from both dinosaurs and modern birds.
Of course, this question of 'kinds' hasn't been of much concern form the layman creationists (this means every on on this site I guess), because he understands the general concept of kind, but not the details of it. But researching creationists have been aware of the problem simply using the word 'kind' without trying to define it has caused, and so it seems as though it is a growing field. You can find here and there articles defining such and such a kind, hopefully in a few years there will be enough of these to have a good overview of it all.
So don't expect me to defend the word 'kind' on here, as I am fully aware that this is a lacking area in creationists litterature.