Re: will be flying(am flying) to New York
You need "I will be" there. The present continuous doesn't work as the future in that context.
By the time you arrive in Seoul, I will be on a plane to New York.
By the time you arrive in Seoul, I will be on my way to New York.
By the time you arrive in Seoul, I will be flying to New York.
Here is a way to use the present continuous but as you can see, it involves a totally different construction:
I am flying to New York on Sunday. I leave two hours before you arrive in Seoul.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.