How to delete music album from iPhone but not from any other devices nor from iCloud
1. Via iTunes

When you sync your iPhone with your main iTunes on a desktop computer, you can simply untick the undesired song/album/artist and hit sync, and it will disappear from your iPhone.



Image from HowToISolve

In this example, ticking Ke$ha will include it, and unticking will exclude it from your phone iTunes library.

2. Directly on your iPhone

Go to Settings &gt; General &gt; iPhone Storage &gt; Music &gt; Edit to delete artists, or ... &gt; Music &gt; Song &gt; Edit to delete songs locally on your iPhone. 



Image from my iPhone

Be aware that those files will be included should you sync your phone again.