[SalesForce] Unable to open primarytab Console Toolkit Integration

You can direct a user to a console link that will open a specific record as a primary tab with a URL like this

http://yoursalesforceurl/console#%2F003xx0000012345

You would need to already know the contact ID though. If you are building an external link with only a phone number, you could point that link to a page with an apex controller that looks up the contact and then redirects the user. That path might look something like this:

User clicks a link to http://yoursalesforceurl/console#%2Fapex%2FgotoContact?phone=1234567890

The page named gotoContact is something like this

<apex:page controller="myController" action="{!redirect}"></apex:page>

The apex class myController has a method that looks like this

public PageReference redirect() { 
    String phone = ApexPages.currentPage().getParameters().get('phone');
    String contactId = [SELECT Id FROM Contact WHERE Phone:=phone][0];
    PageReference pr = new PageReference('yoursalesforceurl/console#%2F'+contactId);
    return pr; 
}

See also:

https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_system_pagereference.htm

https://developer.salesforce.com/docs/atlas.en-us.pages.meta/pages/pages_compref_page.htm

VF controller redirect to another page

Here is a small experiment as a proof of concept to emit events from lightning component and handle in VF

<aura:component>
 <div> Hello World !!!! </div>
  <aura:registerEvent name="myevent" type="c:myEvent" />
  <ui:button label="fireEvent" press="{!c.fireevent}" />
</aura:component>

The JS controller file

({
 fireevent: function(component, event, helper) {
    var myEvent = $A.get("e.c:myEvent");
    myEvent.setParams({"data":"Test"});
    myEvent.fire();
  }
})

The Event file

<aura:event type="APPLICATION">
 <aura:attribute type="string" name="data" />
</aura:event>

The application file

<aura:application access="GLOBAL" extends="ltng:outApp">
  <aura:dependency resource="c:myComponent" />
</aura:application>

The visualforce where event is handled

<apex:page showHeader="false" sidebar="false">
<apex:includeLightning />
<div id="lightning"> Hello world VF ..!!! </div>
<script>

    $Lightning.use("c:myEventApp", function() {
        $Lightning.createComponent("c:myComponent", {}, "lightning", function(){
            $A.eventService.addHandler({ "event": "c:myEvent", "handler" : visualForceFunction});

        });
    }); 

</script>

<script>

var visualForceFunction = function(event){
        var myEventData = event.getParam("data");
        console.log(myEventData);
    };

</script>

DISCLAMIER : I have not tried inside service console but this should help you get started .For ISV apps since this is not documented anywhere ,consult SFDC security review team or salesforce lightning component product team to see if this is right way of doing this .