How to get application reconsidered

Unless an error has been made, (very unlikely, but possible), they won't reconsider an academic decision. if it's still your preference, it's worth getting feedback and seeing what, if anything, you could do to improve your chances if you were to reapply in the next cycle.

I have 2 questions
Will they really not reconsider if I have new relevant experience and better grades (I didn't take Maths AA HL but took the Dutch VWO course to substitute it)?
Also
Regardless, will there be an opportunity to do clearing?

Unis aren't obliged to consider anything that wasn't included in the original application. (Otherwise they'd find themselves in a position where half of unsuccessful applicants would produce more evidence in support of reconsideration). For a lower ranked uni they might be willing to look again, but for KCL they're not going to struggle to fill the course if they don't revisit people. You can try, and have nothing to lose by politely asking, but I'm just setting your expectations that in nearly all cases it will be a no. (NB. I'm not sure if you met the subject requirements with your original application which may colour things a little. Again, worth a try if nothing else.)

Clearing depends on the results of other applicants as well as the general popularity of the course so is impossible to say. I would say less likely for KCL though.

Thank you for the response.
Do you know when information regarding clearing would become available?

5th of July this year.

NB. If the course is closed on UCAS now there is almost no chance it will go into clearing. If it stays open, then there is a possibility.

On UCAS how would I be able to tell if a course is open or closed?