At the very beginning of one's jazz studies, swing feel is the first and most basic thing, which the student comes in contact with.
The musician learns what the swing feel is, analyzing the triplet eighths, in order to understand the origin and the certain "feel" that the swing eighth notes have and begins to further deepen into the concepts of the terms "time" and groove. 
He/she practices on the "swing reading" of a score since the rhythmic values acquire another dimension and require different articulation, compared to reading a score of classical music. And of course all the above are being practiced within the singing process, as the actual experience is the only way to fully grasp the certain sense that "swing feel" has and to achieve singing "in the swinging groove". 

In order to be "solid" into the groove, one has to become fully aware of syncopation, to have a clear sense of the "downbeats" and "upbeats" within the bars, in order to be able to accent the upbeats, exactly where they are placed within the "pulse", given that in the triplet eighth feel (swing feel) the note falling on the downbeat (ie the tied first two eighth notes of the triplet) lasts twice as long (compared to the note falling on the upbeat) and has to be legato... whereas the upbeat (which is the third eighth note of the triplet) is shorter (as it lasts the 1/3 of the beat) yet emphasized.

It is therefore very important to practice the swing feel using the metronome (which will initially click all the beats of the measure, ie the four quarters in a 4/4 measure), that will ensure a steady pulse (beat), called "time", within which the singer will have to "lay" the swing eighths, knowing well that the downbeats must be legato and the upbeats accented. 
Simple though this may sound in theory, it is quite difficult to achieve, when it comes to action. And it can get even harder if the metronome is set to tick only on beats 2 and 4 and when the text is getting more demanding, ie if there is a more complicated rhythmic succession than just a simple row of eighth notes. 

Therefore, when the singer starts phrasing, it is extremely important to accent the upbeats where they need to be emphasized (respecting the legato downbeats), so that there is no rhythmic "dirt" in the groove. 
A continuous legato with too much laid-back feel, within which any attempt for accenting upbeats falls on the "cracks" of the groove, cannot certainly be considered as an interesting rhythmic phrasing! 
Nor the interpretation of a jazz standard, as an exact quote of the original score (as if it was a classical piece) without any phrasing, swing feel and without taking into consideration the rules that syncopation imposes, can be regarded as jazz singing! 
(At this point, you can read the article "Jazz means improvisation".)

It is also very common for a musician/vocalist to be rushing the groove (maybe because of his/her excessive zeal to continuously create motivations for syncopation, ie. for accenting upbeats), by not playing the downbeats for as long as they should last, resulting in an un-grooving, stressful situation, that sounds like "hiccups" and bears no resemblance at all to the relaxed yet grooving swing feel.

There are many ways and number of exercises for practicing syncopation and swing feel. Just be patient and willing to deepen and study this seemingly very simple yet so essential first step in jazz music!
Because playing (especially swing, be bop or hard bop style) without swing feel, syncopation, jazz articulation and phrasing is rather a mockery than jazz playing at all.

Suggestion for studying - Exercises for syncopation from Ted Reed's book "Syncopation for the modern drummer".