Hi @haleyradt24,
Do you use the "SharePoint item approval with a more information option" built-in template to create your flow?
I have made a test and the issue is confirmed on my side. I could only see the Approve option and Reject option within my Outlook mailbox or Approval center. I think this issue is related to this built-in template ("SharePoint item approval with a more information option").
Thanks for your feedback, I would post this issue to my product team, if this issue is solved, I would reply here. Besides, the third option is not available within the approval email sent via the "Start an approval" action in Microsoft Flow currently, if you would like this feature to be added in Microsoft Flow, please submit an idea to Flow Ideas Forum:
https://powerusers.microsoft.com/t5/Flow-Ideas/idb-p/FlowIdeas
In addition, if you want to send an approval email with multiple options (more than 2 options), you could consider take a try with the "Send email with options" action of Office 365 Outlook connector.
More details about the "Send email with options" action, please check the following article:
Send email with options
Please check and see if the following article would help you understand the "Send email with options" action:
https://powerusers.microsoft.com/t5/Building-Flows/Flow-approvals-with-a-Approved-Partial-amp-Reject/m-p/95249/highlight/true#M9340
Best regards,
Kris