In order to get the VAT codes to sync with dimensions you need to follow the following steps:
In the ribbon view within Dimensions, click on System.
Now click on data utilities (If you have permission it will be found to the far right of the ribbon view).
Now click on Synchronise aCloud Data, you can leave everything ticked and when happy hit the Green Tick.
When the above is done you should be able to find the VAT codes as expected in Expense.