Multiple Cloud accounts. I have my cloud account. A client now has Cloud for teams. Is there any way for me to be granted access to their assets without being a member of their team and keep using my own adobe account?

From the CC Assets site at https://assets.adobe.com you can use Send Link (and Save to Creative Cloud) or Collaborate for sharing files.

Send Link provides a read-only view of the files. If Allow Download is checked then you can make your own independent copy of the files using Save to Creative Cloud which shows as a button on the public link page.

Collaborate provides a read and write view of the files. Changes made to the collaborated folder show up for everyone. Collaborate also works with the file syncing that is part of the Creative Cloud desktop application.

Help document on Collaboration: Collaborate on folders and libraries from Creative Cloud account

Help document on Send Link: https://helpx.adobe.com/creative-cloud/help/share.html