Ucas extra kcl havent heard anything

Why did you think that you had more chance through Extra than as a late application?
Have you phoned them up?

They just rejected me saying my qualifications aren’t recognised. However in my previous application they clearly did accept it and even sent me an email saying they recognise it for direct transfer for 1st year.

If the previous application was this cycle, send that guidance back to them and ask them to clarify.

Yes it was. Could you help me in term of drafting it if that’s ok please?

It doesn’t need to be anything fancy, it’s always better to be matter of fact rather than accusatory.
“Thank you for your feedback regarding my application to COURSE. I was confused regarding the guidance that my qualifications were not suitable for consideration for the course, as I’d been advised otherwise when looking to apply earlier in the same cycle, (see attached/below). I’d appreciate it if you could clarify whether the feedback given, or previous advice, was in error or whether any reconsideration would be possible.
Thank you for your time and assistance. Please do let me know if any further information is required.”

Hey, just got a reply from them but it still doesn't explain anything.
Thank you for your message requesting feedback on your application.The Mathematics with Management and Finance BSc (Full-time) here is very competitive, with many of the candidates for this programme typically meeting or exceeding the entry requirements. Due to the high level of applications received for this programme and the limited number of places, your qualifications are not acceptable for direct entry to this programme. I am afraid we are unable to reconsider your application for this programme, but would like to wish you all the best with your applications elsewhere. Best wishes,Reet MKing's Advisor, Faculty Of Natural & Mathematical Sciences (Ug)
it doesn't address that I was considered previously for the same cycle and same qualifications. I wrote exactly and a bit added as to what you said and still didn't get a just answer.

Hey, just got a reply from them but it still doesn't explain anything.

Thank you for your message requesting feedback on your application.The Mathematics with Management and Finance BSc (Full-time) here is very competitive, with many of the candidates for this programme typically meeting or exceeding the entry requirements. Due to the high level of applications received for this programme and the limited number of places, your qualifications are not acceptable for direct entry to this programme. I am afraid we are unable to reconsider your application for this programme, but would like to wish you all the best with your applications elsewhere. Best wishes,Reet MKing's Advisor, Faculty Of Natural & Mathematical Sciences (Ug)

it doesn't address that I was considered previously for the same cycle and same qualifications. I wrote exactly and a bit added as to what you said and still didn't get a just answer.

I'd respond and say, "Thanks for your response. However this hasn't addressed the contradictory guidance I was given on DATE. Could you please clarify?".

Thank you for your message.
We have provided feedback on our decision-making process and the reason for the unsuccessful decision on your application. Unfortunately, we will not be reconsidering this decision and cannot provide you with any further information.  
If you are considering reapplying to King's in the next admissions cycle, we recommend that you check the entry criteria on our webpages, as these can change from year to year. This will be fully updated in the September before the deadline to apply. Further information can be found on the link below: https://www.kcl.ac.uk/study/undergraduate/index.aspx We thank you for applying to King's College London and wish you every success with any other applications you are making.  Best wishes, Reet King's College London Admissions

I'd reply with "I appreciate that I cannot be reconsidered and this was not what I requested with my last message. Only for further guidance as to whether I misunderstood the guidance provided on DATE, whether the guidance itself was faulty, or whether the feedback being given (regarding qualifications not being suitable for entry) is incorrect. As you've advised that you are unable to provide with me any further information relating to the application I should be grateful if you could direct me to the formal complaints process".
The complaints process will be public and you could find it yourself, it's just to give them one last chance to give you something of substance.
If you want to complain that is up to you, but it doesn't sound like they'll be budging.
Another option would be to submit a subject access request for anything relating to your two applications. A bit nuclear and at some point you have to ask whether you would even want to attend there even if they reversed their decision.

what is a subject access request?