How can I view data on my work Apple ID account?

You may find it convenient to collaborate with your other ID as outlined in this document --> Share notes and collaborate on iPhone - Apple Support and a related article If you can't share or collaborate in the Notes app on your iPhone or iPad - Apple Support

I won't copy and paste the instructions here because my browser makes a real mess of the formatting. ;-)

Josephfromva Said:

"can I see notes from two different Apple ID accounts on my iPhone? Say my work Apple ID and my personal Apple ID?"

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Signed In Simultaneously:

No. You can only be signed in to one Apple ID on a device at a time.

View iCloud:

See if you can view these while in iCloud: https://www.icloud.com/notes