To Embed Flow in Salesforce Lightning Web Component, lightning-flow tag can be used. Check the following sample Lightning Web Component and Flow for reference.

Sample Flow:

Salesforce Flow Welcome Screen Configuration:

Salesforce Flow Input Variables Screen Configuration:

Salesforce Flow Output Variables Assignment Configuration:

Salesforce Flow Finish Screen Configuration:

Sample Lightning Web Component:

HTML:

<template>
    <lightning-flow
        flow-api-name="Sample_Screen_Flow"
        flow-input-variables={flowInputVariables}
        onstatuschange={handleStatusChange}>
    </lightning-flow>
</template> 

JavaScript:

import { LightningElement, api } from "lwc";

export default class SampleFlowComponent extends LightningElement {

    @api recordId;

    get flowInputVariables() {

        return [
            {
                name: 'Test1',
                type: 'String',
                value: 'Sample1'
            },
            {
                name: 'Test2',
                type: 'String',
                value: 'Sample2'
            },
            {
                name: 'recordId',
                type: 'String',
                value: this.recordId
            }
        ];

    }
    
    handleStatusChange(event) {

        console.log( 'Status is ', event.detail.status );
        console.log(
            'outputVariables are ',
            JSON.stringify( event.detail.outputVariables )
        );
        if ( event.detail.status === 'FINISHED' ) {
            
            console.log( 'Flow Completed' );

        }

    }
    
}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>56.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__RecordPage</target>
    </targets>
</LightningComponentBundle>

Output: