You can connect your Showcase IDX to kvCORE through Zapier. This will send new leads and new messages (but not search activity) in a one-way outbound connection into kvCORE.
kvCORE is not an official application on Zapier and requires an invite link to set it up. You can access the invite link here.
Zapier has plenty of helpful articles to walk you through setting up Zaps and is a great place to start once you've accessed the invite link above.