Install multiple apps from Play Store with single click
Unless you're from Google, you can't, and for good reasons why Google prohibits it.

I assume you want to do this for better user-experience, in which they can conveniently install what they need with their consent. However, let's put aside that idea and think another possibility: a seemingly-safe app can install rogue apps from Play Store automatically without user's consent!

There's a more detailed explanation on an answer by ozbek on Stack Overflow, in which you can only request Play Store to install an app silently if your app is signed by Google.