Celebrate homecoming, initially drawing flak at Little Chef, sadly (4,3,6,4)

I believe the answer is:

kill the fatted calf

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'celebrate homecoming initially drawing flak at little chef sadly' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'initially drawing flak at little chef sadly' is the wordplay.
'initially' says to take the initial letters.
'sadly' is an anagram indicator.
The first letter of 'drawing' is 'd'.
'd'+'flak'+'at'+'little'+'chef'='dflakatlittlechef'
'dflakatlittlechef' is an anagram of 'KILL THE FATTED CALF'.

Can you help me to learn more?

(Other definitions for kill the fatted calf that I've seen before include "celebrate homecoming?" , "Dispatch podgy young Kerry" , "Celebrate extravagantly" .)

I've seen this clue in The Times.

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