You can make a nanoflow that looks something like this:
If you don't have the month numbers in the database, you can fiddle around with parseDateTime() and formatDateTime() functions to get the correct month instead, but since it's only 12 values it might be easier to just add them manually.
I am just giving sample logic in microflow to calculate month. Logic will be same like Eline told.
Create new entity for Month which stores month number and month name.
In microflow, Retrieving selected Month and Number of months to be added.
From the selected month object, i will retrieve selected month number. Then I will add the selected month number + number of months to be added + 1 to get the month as per your requirement. Once number is retrieved, i will retrieve month object using number. Then I will update that month in calculated month attribute.
As Eline told, Once your addition is done, If your result is > 12, then subtract it from 12 to get required month.