Happy to help.
There are advantages and disadvantages to all of the approaches. linked servers can help reduce data duplication. SSIS can allow you to transform the data as you go. And having the application handle pushing data to both sources helps ensure data consistency.
But they all have disadvantages too. Having the application push the data to both systems, what do you do if one of the 2 data pushes fails? Do you retry the push? Do you undo the first data push? Something else?
Linked server, if the server becomes unreachable, the data becomes unreachable too.
SSIS needs to be scheduled, so you have no "realtime" data there.
Which solution you use depends on which solution fits your needs and which risks you can work with (or around).