The blockchain.info API allows for information about a particular Transaction to be queried by its ID. But if you want to follow the coins to the next transaction, I don’t see what the next query should be.
Each “out” of the transaction has an address associated with it, and you can inquire for details of recent address transactions. But if you explore deep in the past, the latest 50 transactions for a particular direction will not get the expenditure on that particular “out”.
So is there another API available that allows you to query Transaction Details based on “transaction N. as an ‘in’ “? Or do I need to go through the blockchain and make my own storage?
Edit: Blockchain.info obviously has the link to the transaction that expended a certain output in their database, as the HTML view of a transaction has “spent” tags after spent outputs, which are links to the next transaction. However, that particular piece of data in API’s view is not of the same transaction.