$delivery = $quote->getShippingAddress();
$delivery->setSameAsBilling(true)
         ->setCollectShippingRates(true)
         ->collectShippingRates()
         ->setShippingMethod('flatrate_flatrate');

public function apply($cartId, $carrierCode, $methodCode)
{
    /** @var MagentoQuoteModelQuote $quote */
    $quote = $this->quoteRepository->getActive($cartId);
    if (0 == $quote->getItemsCount()) {
        throw new InputException(__('Shipping method is not applicable for empty cart'));
    }
    if ($quote->isVirtual()) {
        throw new NoSuchEntityException(
            __('Cart contains virtual product(s) only. Shipping method is not applicable.')
        );
    }
    $shippingAddress = $quote->getShippingAddress();
    if (!$shippingAddress->getCountryId()) {
        throw new StateException(__('Shipping address is not set'));
    }
    $shippingAddress->setShippingMethod($carrierCode . '_' . $methodCode);
}

object(MagentoFrameworkExceptionStateException)[1380]
 protected 'phrase' =>
  object(MagentoFrameworkPhrase)[1382]
    private 'text' => string 'Shipping address is not set' (length=27)