I would like to add an approval button on the list view of a record that allows

Which version of Appian are you in now?
Records are static and you have to use "Related Actions" and pass on the key information to a process model and have buttons for approval or any business logic.

A sample here shows , you select an employee and update phone#, likewise you can have Approve/Reject etc.
Refer: forum.appian.com/.../Records_Tutorial

I am not sure I understand what you are asking. Tasks require action, record listings show data. To act on those data points, you need to have a task (which you can add allow inline approval) or a related action to start a new process instance that can contain a user input task.
Can you clarify what you are asking to do?

You could acheive this by creating a tempo report based on a portal task list (see the Portal to SAIL plugin). You can use SAIL expressions to build the list of tasks and therefore each one could have the approve/reject button. From the button click you could use the "Run Process Expression Function" plugn to call a process model which would then be able to send messages to your task processes and update them.

This is obviously quite an advanced approach using multiple plugins so use caution when considering your options i.e. is the Appian default behaviour really not an option?

List view in Record cannot be modified to add controls (such as buttons) at the moment. Reading your requirement, I believe you are trying to use List view as a Task list. You should use [Task] to do the same and you can use a Custom Task Report that'd appear as a new view under [Task] should you wish to segregate this functionality to a certain set of people.
see: forum.appian.com/.../Task_Report_Tutorial

You guys are correct, I was trying to add a button to the Task view to approve and not to the Record view to approve, I simply had the two views confused. Thanks!