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In this book we study flags of singular holomorphic foliations, formed by two foliations. We are interested in investigating characteristic classes for this structure and its consequences. In this work we develop a residue theory for these flags. Then, we prove a Bott vanishing theorem for flags. Next we proved a Baum-Bott type theorem for flags. We treat also the Bott rationality conjecture for flags. In this sense we define the Nash residue for flag utilising Nash construction adapted for flags. With this we can do the comparison of the Bott residue and Nash residue for flags, which show the rationality of residues in this context. In the last chapter we deal holomorphic foliations. For this purpose, we present an effective way to calculate residues of the foliations, when the dimension of singular set of the foliation is one less than the dimension of the foliation. This result generalizes the result of Bott.