Hello, and thanks for your question!!
The 2 most common reasons that a toilet will flush on its own are the following.
1- The flapper or fill valve are letting water into the bowl. When the water level in the bowl reaches a certain level, it will cause the toilet to flush.
2- If the plumbing venting in the house has restrictions (blocked or not allowing proper air flow) when another toilet, washing machine, dish washer are used they can cause a suction action in the drain system that can cause the toilet to flush also.
I would try installing a complete flush kit first before anything else.
I hope this answers your question, If so please click the green accept button. If not Im still here to assist you.