There aren’t any apps available in the BB10 app store or Amazon Android app store (including Fing and Ping IP) that are capable of sending ICMP pings. This is in part because at present BB10 OS 10.3 implements Android API level 18 a.k.a. Android 4.3 Jelly Bean, which even on an Android phone generally requires root to send ICMP pings on Android 4.3.
There is a BB10 native way to send ICMP pings, and it doesn’t require an app, since it’s built into the Settings menu. Despite it being under the WiFi menu, you can send pings when on or off WiFi on the mobile data 3G / 4G network.
You can send ICMP pings under BB10 under
Settings → Network and Connections → WiFi → Advanced → Diagnostic Information → Ping`