If I've set up a Financial Type of In-Kind Donation, how should I properly set up the required Payment Instrument?
In order for the 'In-Kind' financial account to show as an option when you setup a new payment instrument it needs to be setup as an Asset account.

You should review the account relationships (under Financial Types) to make sure they meet your needs.

Depending on your accounting setup and reporting requirements I recommend looking closely at this setup to assure you get the results you require.

Hope this Helps!