As salam alaikum, After Friday prayers, I usually recite Surat "Al Kahf" & Surat "Al Yasin" and in my supplication ask the Almighty Allah (swt) to bestow "Thwaab" to my parents & other close relativves (Allah Erhum Hum). Is this appropriate and permissible.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

There is a great reward for reciting the Quran.  It is better for a person to arrange a schedule to recite the whole Quran, as regards specifying a specific chapter at a particular time, then there must be textual evidence for this.  There is evidence that chapter 18 [Al-Kahf] should be recited on a Friday, but there is no evidence –as far as we know –for reciting Yaa Seen [chapter 36] precisely on a Friday.  Therefore, in our view, you should continue the recitation of the entire Quran instead of reciting this chapter only.

For more benefit on the virtue of reciting chapter Al-Kahf and some other chapters, please refer to Fatwa 84014, and to Fatwa 86828 on reciting the Quran on behalf of the dead.  

Allaah Knows best.