orders = [
{id_service: "1", id_empresa: "9", nome_service: "Servico 01", qtd: "0", checkup: "false", price_service : "250"},

{id_service: "2", id_empresa: "9", nome_service: "Servico 02", qtd: "0", checkup: "false" price_service : "300"},

{id_service: "3", id_empresa: "9", nome_service: "Servico 03", qtd: "0", checkup: "false" price_service : "400"}
]

calc(i) {
  let obj = JSON.parse(this.orders[i].price_service);


  if (this.orders[i].qtd == 0) {
    this.result.push(obj);
    this.orders[i].qtd = 1;
  }
  else {
    this.result.splice(i, 1);
    this.orders[i].qtd = 0;
  }
  this.result.reduce(function (a, b) {
    return a + b['obj'];
  }, 0);

}

<div *ngFor="let item of orders; let i = index; ">
    <ion-item>
      <ion-label class="title">{{item.nome_service}}
        <span>{{item.price_service}}</span>
      </ion-label>
      <ion-checkbox (click)="calc(i)" checked="{{item.checkup}}" color="green"></ion-checkbox>
    </ion-item>
    <p>{{result}}</p>
  </div>