Programatically create an order in Magento 2.1

create.php

<?php
/**
 * @author    Frank Clark
 */
namespace Vendor\Namespace\Model\Subscription\Order;

class Create
{
    public function __construct(
        \Magento\Framework\App\Helper\Context $context,
        \Magento\Store\Model\StoreManagerInterface $storeManager,
        \Magento\Catalog\Model\Product $product,
        \Magento\Quote\Model\QuoteFactory $quote,
        \Magento\Quote\Model\QuoteManagement $quoteManagement,
        \Magento\Customer\Model\CustomerFactory $customerFactory,
        \Magento\Customer\Api\CustomerRepositoryInterface $customerRepository,
        \Magento\Sales\Model\Service\OrderService $orderService,
        \Magento\Quote\Api\CartRepositoryInterface $cartRepositoryInterface,
        \Magento\Quote\Api\CartManagementInterface $cartManagementInterface
    ) {
        $this->_storeManager = $storeManager;
        $this->_product = $product;
        $this->quote = $quote;
        $this->quoteManagement = $quoteManagement;
        $this->customerFactory = $customerFactory;
        $this->customerRepository = $customerRepository;
        $this->orderService = $orderService;
        $this->cartRepositoryInterface = $cartRepositoryInterface;
        $this->cartManagementInterface = $cartManagementInterface;
    }

    /**
     * Create Order On Your Store
     *
     * @param array $orderData
     * @return array
     *
     */
    public function createOrder($orderData) {

        //init the store id and website id @todo pass from array
        $store = $this->_storeManager->getStore();
        $websiteId = $this->_storeManager->getStore()->getWebsiteId();

        //init the customer
        $customer=$this->customerFactory->create();
        $customer->setWebsiteId($websiteId);
        $customer->loadByEmail($orderData['email']);// load customet by email address

        //check the customer
        if(!$customer->getEntityId()){

            //If not avilable then create this customer
            $customer->setWebsiteId($websiteId)
                ->setStore($store)
                ->setFirstname($orderData['shipping_address']['firstname'])
                ->setLastname($orderData['shipping_address']['lastname'])
                ->setEmail($orderData['email'])
                ->setPassword($orderData['email']);

            $customer->save();
        }

        //init the quote
        $quote=$this->quote->create();
        $quote->setStore($store);

        // if you have already buyer id then you can load customer directly
        $customer= $this->customerRepository->getById($customer->getEntityId());
        $quote->setCurrency();

        $this->cartRepositoryInterface->save($quote);

        $quote->assignCustomer($customer); //Assign quote to customer

        //add items in quote
        foreach($orderData['items'] as $item){
            $product=$this->_product->load($item['product_id']);
            $product->setPrice(22);
            $quote->addProduct(
                $product,
                intval($item['qty'])
            );
        }

        //Set Address to quote @todo add section in order data for seperate billing and handle it
        $quote->getBillingAddress()->addData($orderData['shipping_address']);
        $quote->getShippingAddress()->addData($orderData['shipping_address']);

        // Collect Rates and Set Shipping & Payment Method
        $shippingAddress = $quote->getShippingAddress();

        //@todo set in order data
        $shippingAddress->setCollectShippingRates(true)
            ->collectShippingRates()
            ->setShippingMethod('flatrate_flatrate'); //shipping method
        $quote->setPaymentMethod('checkmo'); //payment method

        //@todo insert a variable to affect the invetory
        $quote->setInventoryProcessed(false);



        // Set sales order payment
        $quote->getPayment()->importData(['method' => 'checkmo']);

        //$quote->save();
        $this->cartRepositoryInterface->save($quote);

        // Collect total and saeve
        $quote->collectTotals();

        // Submit the quote and create the order
        $quote = $this->cartRepositoryInterface->get($quote->getId());
        $order = $this->cartManagementInterface->submit($quote);

        //do not send the email
        $order->setEmailSent(0);

        //give a result back
        if($order->getEntityId()){
            $result['order_id'] = $order->getEntityId();
        }else{
            $result=['error'=>1,'msg'=>'Your custom message'];
        }

        return $result;
    }
}
?>

Creates order but all prices sets to 0 after adding line $this->cartRepositoryInterface->save($quote); after $quote->setCurrency();

@godriccao your solution works, thanks a lot.

@godriccao , shipment is not getting saved