Hi Jennifer, without knowing your specific use case it's hard to provide detailed guidance, but long story short you can access any related record from a flow.
Your architecture is going to matter a lot here - updating a parent is much simpler than updating a peer or finding the right child record to update.
If Checklist Items is linked to whatever you're tying the files to via a lookup, you can just navigate directly to it from within the flow ($Record->Checklist Item>[field]).
If Checklist Items is a child of whatever you're tying the files to -- that is, the file is attached to Contact, and Checklist Items is ALSO attached to Contact, and you have several Checklist Items for any one Contact -- then you will need to use the Get Records action to find your checklist item record before you can modify it.