My issue is very similar if not the same as this issue.
Zapier offer a way to connect to JIRA Cloud but for some strange reason it wont authenticate successfully.
The below screen is what I end up seeing and seem to have no way to get past it.
"You don’t have access to this app.
This application is in development - only the owner of this application may grant it access to their account."

Is anyone aware of fix for this? I am the owner of both accounts; Zapier and Atlassian but am not sure how to grant the suggested access.
I spoke to Zapier too and they said that they're pursuing to apply for "public" status for their OAuth app but this is yet to come through from Atlassian.
However, there surely must be a workaround until the two of them (Zapier<>Atlassian) sort out the OAuth differences.. or is there not?