Prevent notifications from other apps when specific app is running

"Do Not Disturb While Driving" mode will be available in iOS 11. So a few more months patience and you have the feature you want.

“It’s all about keeping your eyes on the road,” Apple Senior Vice President of Software Engineering Craig Federighi said when introducing the feature at WWDC in June. “When you’re driving, you don’t need to respond to these kind of messages. In fact, you don’t need to see them"

Your iPhone will detect when it's in a driving car and put your phone on "Do Not Disturb While Driving" mode. You can also manually turn it on/off via Control Centre.