Hello, I have just finished my first year as a BSc Economics student at King's.
To answer your question regarding the flexibility of the content of the course, I would say that in the first year there is no flexibility as you don't get to choose your modules. However, the course is jointly run by two departments: the Department of Political Economy and King's Business School. This implies hat students studying the course have compulsory and optional modules (in the second and third year) from both departments which can be considered an advantage.
In the second year, you have 4 compulsory modules from both departments and you need to choose 4 optional modules from either of the two departments. Talking from personal experience however, we had 15 module options from the Department of Political Economy (which were mostly Politics based) and only 5-6 options from the Business School. This can be considered as a disadvantage by someone who is more interested into the Management, Accounting or Finance side of Economics, rathe than the Politics side. However if you are interested in Politics then you would find the course content 'flexible' with lots of Politics-related options. You can always apply to modules provided by other deparments at the university, however there is a whole process where you need to get your department's permission, as well as the persmission of the department of the other module and it is also based on availability and perhaps any pre-requisites that the module has.
Hope this helps, let me know if I can help with anything else!