Hi @diyninja,
Could you please share a screenshot of your flow's configuration?
Do you send the approval emails using the "Start an approval" action?
I have made a test on my side and don't have the issue that you mentioned. When my flow runs, the approval email takes about 10 seconds to arrive in my Outlook inbox.
If the approval email takes a long time to arrive in your Outlook mailbox, please check if you have set Delay Incoming Message within your Outlook mailbox. Please check and see if the following article would help in your scenario:
https://social.technet.microsoft.com/Forums/en-US/297c332a-916a-4cc9-8a4b-15cf6f765ae3/receiving-emails-delayed-in-outlook-office-365-environment?forum=officeitpro
In addition, please take a try to re-create your flow and try it again to check if the issue is solved. In addition, please consider close your Outlook client and re-open again, then try your flow to check if the issue is solved.
Best regards,
Kris