When the Articles are attached to Salesforce Chat Transcripts, it will be stored in LinkedArticle Object/Entity. When the Articles are attached to Salesforce Cases, it will be stored in CaseArticle Object/Entity.

So, we can develop a record-triggered flow on LinkedArticle object/entity to fetch the Chat Transcript Case and create the CaseArticle.

In the following Sample Flow,

1. We are triggering the flow when a Linked Article is created. It means when the Article is attached to the Chat Transcript.
2. We are fetching the Chat Transcript record using Get Records element.
3. We are creating Case Article record to link the Article to the Case record of the Chat Transcript.

Sample Flow:

Fetch Chat Transcript Configuration

Create Case Linked Article

SOQL for LinkedArticle:

SELECT Id, LinkedEntityId
FROM LinkedArticle

SOQL for CaseArticle:

SELECT Id, CaseId
FROM CaseArticle

If you have an use case to detach articles detached from the Chat Transcript from the Case in Salesforce, check the following:

How to detach articles detached from the Chat Transcript from the Case in Salesforce?