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Thanks for reaching here! If I have understood right you want to deploy from local git with SSH key instead of ID/PW authentication, If so below is the explanation.
As SSH URL for kudu repository (https://<sitename>.scm.azurewebsites.net:443/<sitename>.git) should be needed to achieve that however Kudu support local git deployment with a SSH key is not currently.
-Local git service is SCM which only https (not SSH protocol).
-SCM authentication only support basic and AAD – not SSH-RSA (or alike) key-pair.
For GitHub/Bitbucket/GitLab you can set up an SSH 'deploy key'
See: https://github.com/projectkudu/kudu/wiki/Continuous-deployment#for-private-repos-set-up-a-deploy-key
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