You can re-download an app directly from the App Store using the procedure in the "On an iPhone, iPad, or iPod touch" subsection of the "Redownload apps" section of:
Redownload apps, music, movies, TV shows, and books from the iTunes Store, iBooks Store, and App Store - Apple Support
FYI, just because it has a cloud symbol (as in step 4 of the above subsection) does not mean it is coming from the cloud. The "cloud" does not have any of your apps (only possibly your app data, i.e., level & position within a game). When you delete the app from your iPhone, that data should be deleted as well. If not, double tap the app (when it is still on your iPhone) and swipe up. That should "initialize" the app.
I suspect the problem you are having relates to why the app stopped working on your iPhone in the first place. You might try restarting/force restarting your phone before you download the app again:
Restart your iPhone, iPad, or iPod touch - Apple Support
If your iPhone, iPad, or iPod touch won't turn on or is frozen - Apple Support (See the "If your screen is black or frozen" section)