Textual response generation is pivotal for multimodal \mbox{task-oriented} dialog systems, which aims to generate proper textual responses based on the multimodal context. While existing efforts have demonstrated remarkable progress, there still exist the following limitations: 1) \textit{neglect of unstructured review knowledge} and 2) \textit{underutilization of large language models (LLMs)}. Inspired by this, we aim to fully utilize dual knowledge (\textit{i.e., } structured attribute and unstructured review knowledge) with LLMs to promote textual response generation in multimodal task-oriented dialog systems. However, this task is non-trivial due to two key challenges: 1) \textit{dynamic knowledge type selection} and 2) \textit{intention-response decoupling}. To address these challenges, we propose a novel dual knowledge-enhanced two-stage reasoner by adapting LLMs for multimodal dialog systems (named DK2R). To be specific, DK2R first extracts both structured attribute and unstructured review knowledge from external knowledge base given the dialog context. Thereafter, DK2R uses an LLM to evaluate each knowledge type's utility by analyzing LLM-generated provisional probe responses. Moreover, DK2R separately summarizes the intention-oriented key clues via dedicated reasoning, which are further used as auxiliary signals to enhance LLM-based textual response generation. Extensive experiments conducted on a public dataset verify the superiority of DK2R. We have released the codes and parameters.