If the array is called value this will sort its items (ascending mode) using start as the key.
{{ value | sort(attribute='start') }}
Paste this into the Template Editor and experiment with it:
{% set value = [
{
"allDay":true,
"color":"brown",
"start":"2019-08-08T00:00:00+02:00",
"title":"P-K"
},
{
"allDay":true,
"color":"grey",
"start":"2019-08-09T00:00:00+02:00",
"title":"Restafval"
},
{
"allDay":true,
"color":"grey",
"start":"2019-08-16T00:00:00+02:00",
"title":"Restafval"
},
{
"allDay":true,
"color":"blue",
"start":"2019-08-21T00:00:00+02:00",
"title":"PMD"
},
{
"allDay":true,
"color":"grey",
"start":"2019-08-23T00:00:00+02:00",
"title":"Restafval"
},
{
"allDay":true,
"color":"grey",
"start":"2019-08-30T00:00:00+02:00",
"title":"Restafval"
},
{
"allDay":true,
"color":"grey",
"start":"2019-01-04T00:00:00+01:00",
"title":"Restafval"
},
{
"allDay":true,
"color":"lightgreen",
"start":"2019-01-04T00:00:00+01:00",
"title":"Kerstboom"
},
{
"allDay":true,
"color":"blue",
"start":"2019-01-09T00:00:00+01:00",
"title":"PMD"
}
] %}
{{ value | sort(attribute='start') }}