In which of his works is the quotation, Duke's son, cook's son, son of
one hundred kings,?"

Dear bigede,

The correct quotation is "Duke's son - cook's son - son of a hundred
kings". It is a line from Rudyard Kipling's poem "The Absent-minded
Beggar", written on 16 October 1899.

You can learn about the background of this poem here [1]:
http://www.sfowler.force9.co.uk/page_10.htm

And you can read the full poem here [2]:
http://www.sfowler.force9.co.uk/page_9.htm

Hope this answers your question!
Regards,
Scriptor



Sources:

[1] History as we write it: The Absent Minded Beggar - An introduction
http://www.sfowler.force9.co.uk/page_10.htm

[2] History as we write it: The Absent Minded Beggar
http://www.sfowler.force9.co.uk/page_9.htm

Search terms used:
"Duke's son, cook's son"
://www.google.de/search?num=20&hl=de&newwindow=1&safe=off&c2coff=1&q=%22Duke%27s+son%2C+cook%27s+son%22&btnG=Suche&meta=
"The Absent-minded  Beggar" kipling october
://www.google.de/search?num=20&hl=de&newwindow=1&safe=off&c2coff=1&q=%22The+Absent-minded++Beggar%22+kipling+october&btnG=Suche&meta=

Quick and deadly accurate.  My wife googled it correctly and came up
with it five minutes after I had sent it in.  Thanks.