Made popular in a recent episode of "The Office", dinkin flicka roughly translates to "That's life" or "C'est la vie".
It can be used in many circumstances and basically means, 'well, what can you do about it?.. that's life'
The expression is generally used in response to horrible circumstances and is often repeated in agreement by the one in the bad situation.
According to the Office, the expression is "something us Negroes say" but dinkin flicka has recently gained popularity among other ethnic groups.
Darryl: I grew up in the hood.
Michael: dinkin flicka.
Darryl: dinkin flicka.
I just got shot!
yea.. dinkin flicka...