I am not very sure if this would fall under MS Flow or under Power BI - but if this is given a try, I am pretty sure, some efforts can be minimized as an admin (considering timezones as well and the wait period).
I have a half baked Security set up and still trying to resolve the gap for my Power BI dashboard. The cycle is when a new user wants to get a hand on the report (RLS enabled), tries to access the dashboard to see the Access Denied message and then raises the request from Power BI Services site. On triggering the request - it is not just the access to the report , access to the data set should also be set based on the access levels, so as an additional step, I have created questionaire using the MS Form that triggers the MS Flow of type Approval / Rejection process. So - here, there will be 2 requests and approvals / rejects required -> 1 for the report and the other for the data set. Would rather look for a single click option to set up a request and responses process.
Attaching the image of the flow that is expected - Can also find the same from the twitter link shared in the post.
It would be even helpful if this can be acheived with the current state of MS Flow / Power BI.