There doesn’t seem to be justify-self, but you can achieve similar result setting appropriate margin to auto¹. E. g. for flex-direction: row (default) you should set margin-right: auto to align the child to the left.
.container {
height: 100px;
border: solid 10px skyblue;
display: flex;
justify-content: flex-end;
}
.block {
width: 50px;
background: tomato;
}
.justify-start {
margin-right: auto;
}<div class="container">
<div class="block justify-start"></div>
<div class="block"></div>
</div>¹ This behaviour is defined by the Flexbox spec.