I've come across a couple of threads on here and posting this to see if anything has changed.
Does SharePoint Online and OneDrive for Business store a file checksum? Looking at other cloud platforms this is available in their APIs.
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SharePoint uses some checksums to determine if 2 documents are the same internally. These checksums are used by search for the duplicate detection.
This has is build in an "undisclosed way" (MS Confidential) which is described here: https://blogs.technet.microsoft.com/fesiro/2013/11/11/sharepoint-2013-search-near-duplicates-and-documentsignature/
Also this signature is not supposed to detect 100% duplicates, but Is aiming for a near duplicate match, which is not the same as a checksum. It can be accessed via search though and is exposed as a managed property (documentsignature).
So you would need to generate one yourself and store it manually for each document. Another thing that will annoy you is that SharePoint might be updating the document once you upload it, in order to add metadata to it (Property promotion) which you wont be able to affect in SPO, which might (most likely) mess with your checksum after you upload it.