Technology to predict responses is a key element in human-to-human messaging that has increasingly been utilized to enable AI-mediated communication. When response suggestions from AI are incorporated into human messaging, it will have an impact on the flow and content of the dialogue. In this paper, we investigated the effect of AI response suggestion sentences used for chat messaging on dialogue flow from two aspects: dialogue act and initiative. Usage rates of response suggestions for different dialogue acts were measured with BLEU scores, and we found that the response suggestions contributed to the establishment of a proper dialogue flow, such as an answer in response to a question. The results of our case study indicated that users who take the initiative in the dialogue tend to utilize response suggestions less frequently. We also found that some written responses were based on the suggested sentence structure but conveyed different messages.