It depends on where the data is saved. If it is saved on the linked in account, you would have to contact them about that and see if they have a way.
If it is stored on your phone, somewhere, or was, then there is no guarantee of retrieving it, but you can try the following.
There are a few apps/programs out there that 'may' be able to help you recover the data.
A few of the programs you could try would be... DiskDigger, MobiSaver, Android-Recovery and Tenorshare. They are all data recovery apps/programs. There are many others out there, so check around and see which you would rather try. There is also one called RECUVA, that I have heard is free, which you could try.
One important note though, most of these programs are not free...