KKR is a publicly traded partnership. As a limited partner of the company you own units, rather than shares. KKR will issue you a K-1 form detailing your partnership distributions and your portion of the partnership's potentially taxable activities. The K-1s were mailed last month; more information here: http://ir.kkr.com/kfn_ir/kfn_taxinfo.cfm
Note that KKR & Co.'s ownership of another partnership, KKR Financial Holdings, is attributed to each of the KKR partners, meaning that while you will receive a single Schedule K-1 you are actually required to separately report your income from KKR and KKR Financial. KKR is pretty good about this and actually provides a very detailed breakdown between the two entities.