To have rhythm and to be succinct together imply poetry, at least in my opinion. I recommend reading not poetry per se, but work that is “equal” in both prose and poetry, more specifically I recommend reading Shakespeare, for he fits this bill apropos his plays. I recommend reading his work often and aloud; the purpose of this is to train your ear as a musician does while also following a structure that tells a story. Again, I am advising you to read his plays more than his sonnets and narrative poems. If you read enough of his work you can see how his style goes in and out of poetry and prose almost seamlessly, and you can see his maturity with this skill in some works more than others. Bear in mind that I am not advising you to imitate, rather, I am advising you to listen and observe when these shifts occur; I am advising you to become familiar with this style.
This, in effect, is not a matter of learning through a book as I think you mean with the elements of style text, rather, it is as a student shadowing a physician: you must see how a craftsman—either in language or medicine—uses his skills not only to vitalize, but vitalize the subject to a state of equality or “good health.” In this case, what you deem “good health” is this union and homogeneity of both rhythm and prose.
I suggest Shakespeare, too, because his work was written in English and therefore not translated; if you do not know, works in their original language maintain an integrity not comparable to translations, thus, Shakespeare is invaluable in this front.
To recap: shadow Shakespeare, train your ear, and then practice. This requires muchnecessitates patience, so sit down, have fun, and let your mind wander as you take your time to read his work.
I hope you fare well in this regard.