Exporting DNS zonefile from Amazon Route 53

It's not possible yet. You'll have to use the API's ListResourceRecordSets and build the zonefile yourself.

The following script exports zone details in bind format from Route53. Pass over the domain name as a parameter to script. (This required awscli and jq to be installed and configured.)

#!/bin/bash

zonename=$1
hostedzoneid=$(aws route53 list-hosted-zones --output json | jq -r ".HostedZones[] | select(.Name == \"$zonename.\") | .Id" | cut -d'/' -f3)
aws route53 list-resource-record-sets --hosted-zone-id $hostedzoneid --output json | jq -jr '.ResourceRecordSets[] | "\(.Name) \t\(.TTL) \t\(.Type) \t\(.ResourceRecords[]?.Value)\n"'