Hi @Stmorgan,
Do you want to incorporate your existing Outlook signature into an email sent via an app?
Could you please share a bit more about your Outlook signature?
I have made a test on my side, if you want to incorporate your existing Outlook signature into an email sent via an app, I afraid that there is no way to achieve your needs in PowerApps currently.
The Outlook signature set within your Outlook would only take effect within an email sent through Outlook, the Outlook signature functionality could not applied to an email sent via an app.
If you would like this feature to be added in PowerApps, please submit an idea to PowerApps Ideas Forum:
https://powerusers.microsoft.com/t5/PowerApps-Ideas/idb-p/PowerAppsIdeas
As an alternative solution, you could consider take a try to initialize a global variable (using Set function) to store the Outlook signature content within your app, then include the global variable within the email body of an email sent from your app:

Best regards,
Kris