I am very far, so I can not come, but for what it is worth will try to give some advise.
Flushing can be a symptom of parasites, or poor water conditions.
Can b e other thing too but this is the first that comes to mind.
To see if it is parasites, U will need to take a scrap and see what it is...in order to treat it. That is if it is parasites.
Malachite green and formaline is a medication that helps in several cases of parasites...but I would not use it until U are sure which one it is or if it is. Your fish is stressed...so better to be sure before treating.
The second possibility is nitrites or oxygen depletion.
Do U clean your filters regularly? What filtration are U using? U said U added new Koi...maybe the system is not able to handle so many koi?
Check your water parameters, buy a kit and report them here.
Check ammonia, nitrites, PH, KH and GH. All those parameters can affect the health of your Koi.
U need to do that as soon as possible, or you will lose more Koi.
Do U have sufficient aeration in your pond? It is hot now and I dont know at what level above sea U are...but oxygen is less soluble in warmer water.
Do U have green water in the pond? That can be a contributing factor.
As immediate solution I would suggest 50% water change...
Do U do weekly water changes? Do U use dechlorinator when doing that?
Please check all this as soon as possible so It is possible to see what the problem is.
Then We can advise from there...
Please do the tests before the water change.