Two-dimensional covalent organic frameworks (COFs) are a versatile class of porous materials that can be tailored for solar energy conversion applications through the incorporation of organic chromophores as linker units. In this work we examine whether such COFs can be engineered to support singlet fission (SF), the generation of two triplet excitons from a single photoexcitation. We simulate the structural and electronic properties of a series of COFs possessing embedded polyacene linkers from benzene through pentacene. Detailed electronic structure calculations suggest that necessary conditions on the energy and electronic coupling for SF can be met with COF architectures closely related to those already synthetically achieved. Molecular dynamics simulations reveal that the embedded acenes preferentially adopt orientations at an angle relative to the COF plane at room temperature, modifying the energy levels and electronic couplings relative to their minimum energy conformations at 0 K. Charge mobility through the COFs is quantified as a function of the length of the embedded acene through application of a recently introduced charge transport index. Implications for the future design of porous materials supporting singlet fission are discussed.