Unmute specific app when iPhone is in silent mode
Short answer:

No, that's not possible with third party apps.



Long answer:

Third party apps can not override the mute switch. It only works for Apple's own "Find my iPhone" app. The only possibility I know of is to jailbreak your phone and to use a tweak that lets you put some apps on a white list. Jailbreaking, however, is not recommended.

You may try to use "Do not disturb". It lets you add specific contacts to a favorites list. Only these contacts will ring with DND enabled.