Is it necessary to replace the part of a flex pipe with another piece or can you use regular exhaust pipe?

No, you should not use regular exhaust pipe to replace a section of flex pipe. Flex pipes are designed to flex and absorb vibrations from the engine and drivetrain. Regular exhaust pipe is rigid and will crack or break quickly under those same stresses. Replacing a section of flex pipe requires a flex pipe section, not a rigid pipe. Using a rigid pipe will likely lead to premature exhaust system failure and potential damage to other components.