Specify the k-options attribute:
<input id="startDate" kendo-date-time-picker
k-ng-model="vm.startDate"
k-on-change="vm.updateStartDate()"
required,
k-options="startDateOptions"
/>
And then implement the options with the disabledDates(http://docs.telerik.com/kendo-ui/api/javascript/ui/datetimepicker#configuration-disableDates) config specified however is appropriate for your situation, i.e.
$scope.startDateOptions = {
disableDates: function (date) {
var disabled = [13,14,20,21];
if (date && disabled.indexOf(date.getDate()) > -1 ) {
return true;
} else {
return false;
}
}
};
Example: http://dojo.telerik.com/@Stephen/eLuWE