Who can edit Service Desk workflows?

[Shannon Condon]

An employee I added as an Admin on the Service Desk site is unable to edit the workflows without my permission. 

[Petter Gonçalves]

Hello @Shannon Condon

Welcome to the Atlassian Community!

In order to edit a workflow, a user must have the following permissions.

1. The Administer project permission. To add it, navigate to the project(s) related to the workflow > Project settings > Permissions and add the user to the related permission. P.S: This permission must be added to all projects related to the workflow.
2. The Global Permission "Administer Jira". Navigate to Settings > System > Global Permissions and add the user with the relevant permission.

If you would like to get more details about the steps above, you can check the following documentations:

Managing project permissions

Managing global permissions 

Let us know if you have any questions.