How to align button right inside Dialog angular material?

You can use the align HTML attribute:

<div mat-dialog-content>
  <p>What's your favorite animal?</p>
  <mat-form-field>
    <input matInput [(ngModel)]="data.animal">
  </mat-form-field>
</div>
<div mat-dialog-actions align="end">
  <button mat-button [mat-dialog-close]="data.animal" cdkFocusInitial>Ok</button>
</div>

Demo

Note: The reason why setting an align="end" attribute works on the dialog’s actions container is because the align attribute is used to add flexbox properties to the dialog actions in the dialog component’s theming SCSS file:

(Extract of dialog.scss)

.mat-dialog-actions {
  // ...
  &[align='end'] {
    justify-content: flex-end;
  }

  &[align='center'] {
    justify-content: center;
  }
}

Here’s the source code.