Unfortunately, your options are limited.
You can create a chat room individually, invite the other user there, and post that link in the comment section. Or you do an uninterrupted ababab comment chain, followed by a prompt for moving the discussion to chat - those are your reliable options. Either you invite them to a chatroom that you create, you ask a mod via a flag, or you go through three iterations of uninterrupted comment exchanges to reliably get there.
Deleted comments in chains count for the three uninterrupted pairs of comments exchange.
Thomas Markov and I did one rapid commenting test, it took us three completed pairs of comments, and the 7th comment would move the discussion to chat; both of us had the prompt after three completed pairs. After that, we tested together with Someone_Evil whether we could use an abc approach. Even after my fourth comment in the chain, we got no prompt. Then we changed to pairs again in the same comment thread, and the three pairs did the trick again, but only I received the prompt as the starter of that chain.
So your best bet is to have an uninterrupted comment chain of three pairs. You might want to tell anybody else to abstain from interrupting your conversation.
This is the most recent feature-request to change something about the status quo: Can the chat message pop-up be inserted after 5 comment "back and forth" argument strategies?
This discussion on our meta goes into why we don't have an autogenerate button for moving comments to chat.
This is the most longstanding and voted-on feature request for an on-demand button: Should "move-to-chat" be provided on demand (as a button perhaps)?