Getting RecordTypeId selected from 'Record Type Selection' Page, in a lightning component that overrides create screen

Summer'18 update provided a new interface 'lightning:hasPageReference'. You can now access the recordTypeId in your controller as below:

var recordTypeId = component.get("v.pageReference").state.recordTypeId;

https://developer.salesforce.com/docs/component-library/bundle/lightning:hasPageReference/documentation

Try using force:createRecord which has a recordTypeId attribute.

var createAcountContactEvent = $A.get("e.force:createRecord");
createAcountContactEvent.setParams({
    "entityApiName": "Contact",
    "defaultFieldValues": {
        'Phone' : '415-240-6590',
        'AccountId' : '001xxxxxxxxxxxxxxx',
        'recordTypeId': "1234455566"
    }
});
createAcountContactEvent.fire();