Dyadic Green's functions (DGFs) for continuously curved waveguides are important for the feeding and radiation problems of cylindrically conformal slotted-waveguide arrays. The major difficulty in the construction of these DGFs in curved waveguides and cavities is that there are no entire-domain TE or TM modes with respect to the curving direction, while the longitudinal-section electric (LSE) and magnetic (LSM) modes do not have the complete orthogonality in terms of the dot product as required by the conventional Ohm-Rayleigh method as practiced in literature. Therefore, the conventional Ohm-Rayleigh method for constructing DGFs is not applicable to curved waveguides. In this work, the DGFs are constructed with the help of the Lorentz reciprocity theorem and the mode orthogonality based on the concept of power flow, and by adding the source singularity terms. To reduce the orders of singularity of DGFs in their application to waveguide walls, the common form of DGFs is then reformulated into a form convenient for numerical computation by both forward and backward derivation procedures. Finally, a general procedure is proposed for the reformulation of DGFs for common types of waveguides. The DGFs derived are applicable to problems with curved waveguide junctions, and coupling and radiating slots for conformal slotted-waveguide antennas.