'no' possessive particle after あか と きいろ の meaning? and why is it needed?

‘no’ possessive particle after あか と きいろ の meaning? and why is it needed?

It’s used as a descriptor. Very similar to な in functionality, though it can also be used with nouns.
For example:
病気の人=a sick person
普通の風邪=a common cold
赤と黄色の花=A red and yellow flower

病気な人、 普通な風邪 or 黄色な花 would be incorrect.

I found some more detailed explanations:
https://www.reddit.com/r/LearnJapanese/comments/2pauh5/what_the_difference_between_a_no_adjective_and_a/

ahh makes sense if a noun is present then it is no but if there is no noun present then we use na, right?

Yeah if it’s not a な or い adjective, の would be correct.