A "potluck", in this context, is nothing more than a meal shared among members of a Church after a service. There's no doctrinal or ritual significance to it, as you know, and it's not ordained. it's simply sharing a meal amongst our Church family.
Jesus often ate with His disciples, so an argument could be made that Christians can trace it there. You could use the miraculous feeding of the multitudes, I suppose. However...
I'm sure the practice of eating after a service or worship, people bringing food, sharing time and a meal together far predates even New testament times. You could probably, if you liked, trace it right back to Adam and Eve eating of the fruit of the Garden (even if only allegorically, as many would interpret that book.) You may as well ask "When did the institution of greeting a brother in Christ" or "shaking hands after the second Hymn get it's start"
The answer is, of course, back at the beginning. It's just what families do. Our Church family, our co-workers, our biological family, or in-laws. We just enjoy spending time with those we care about.
More here: http://www.fbcbennington.org/sermonsjhh/2011/7/15/in-search-of-the-new-testament-potluck-acts-237-47.html
Excerpt:
On this final day of VBS, the adults and the children are exploring
Acts 2:37-47. Right in the midst of these essentials of the Church’s
identity, we learn that we are not the first believers to connect
“food” to the Christian faith. Indeed, the first churches learned
that “breaking bread together” gave them as much a sense of identity
as did the teaching, the praying, and the sharing with one another.
Being together at table is essential to church as any prayer, hymn, or
sermon.
When you think back over your life, do you remember a good meal at
church? I think of the dinner rolls of Anna Brown, a dedicated lay
woman who had a kind word literally for every person around the table
(a feat among Kansas Baptists, who are better known for having
opinions on just about everything and everybody). I recall the
skilled cooking of Orman Halderman, who learned to cook during his
WWII service years, able to rally a fine meal every month out of a
volunteer group of men trying to cook, without Orman’s leadership
otherwise would have brought new meaning to the phrase “green eggs and
ham”. I recollect the kindness shown by the search committee when
coming to visit First Baptist, Bennington, five years ago. You heard
that Kerry was a vegetarian and made especial effort to offer a meal
sensitive to her dietary convictions. That meant a lot. And later
this morning, we will make our way down the hall for the meal that
will recall the words of an old hymn: “feed me till I want no more.”
If you were to claim that “food” is somehow secondary to “church”, I
would disagree gladly. Without meals together, we forget skills and
values that worship cannot impart to us. In the pews, there’s a
formalism that the supper bell sets aside. At table, we get to know
the person beside us in the pews. (A good suggestion for potluck:
Sit down by somebody later today that you have not connected with in a
spell. Breaking bread together is a great icebreaker for churches to
get to know one another. Better yet, find somebody you cannot recall
getting to know yet. It may be a little uneasy at first, but
remember, the person across from you is a fellow congregant. You have
“First Baptist” in common!)