I do not think you can use Gold status with other airlines right now. Only on Singapore airlines can you use it.
[Hypothetically]If at all, Vistara and AI merge (since there are no two airlines from the same country in the same alliance, and then if the Gold status is equivalent to the Star Alliance gold (unless which I believe Vistara may devalue their gold program, or decrease the priority) you can get it on other Star Alliance airlines. This is a long shot and you don't know how much time it will take. But currently, your privileges will be same as of a normal user on other partner airlines (excluding Singapore)