Why upgrade to SQL 2014, a product which is out of mainstream support? Why not SQL 2019? Even SQL 2016 would be a better choice.
First make sure that you have installed SP3 for SQL 2008 R2. Else any attempt to upgrade is likely to fail.
I have not tested, but I would assume that SQL 2008 continues to run on Windows Server 2016, even if it is not supported. Then you can do the upgrade. And don't forget to apply SP3 and CU4 for SP3, if you go for SQL 2014. I would also recommend that you add -T4199 to the startup parameters, to get optimizer fixes. This is particularly important on SQL 2014, as else you do not get the fixes for the issues with the new cardinality estimator. (On the other hand, if you go for SQL 2016 or later, you don't have to bother.)
You should also test the application on SQL 2014 (or which version you go for before the upgrade). There were a few features discontinued with the release of SQL 2012. I don't know what sort of system this is, but there can also be performance regressions. The more important the system is, the more important it is to test.