The phrase "the land of milk and honey" traces back to the bible. In the Old Testament, God makes a promise to give some land to Abraham and his descendants (Genesis 15:18-21):
On that day the Lord made a covenant with Abram and said, "To your descendants I give this land, from the Wadi of Egypt to the great river, the Euphrates— the land of the Kenites, Kenizzites, Kadmonites, Hittites, Perizzites, Rephaites, Amorites, Canaanites, Girgashites and Jebusites."
This land is called the Promised Land (which became a phrase in its own right) or, in other verses, "the land of milk and honey", "the land where milk and honey flow" or similar:
(...) and I have come down to deliver them out of the hand of the Egyptians and to bring them up out of that land to a good and broad land, a land flowing with milk and honey, to the place of the Canaanites, the Hittites, the Amorites, the Perizzites, the Hivites, and the Jebusites.
(Exodus 3:8, emphasis mine)
If the Lord delights in us, he will bring us into this land and give it to us, a land that flows with milk and honey.
(Numeri 14:8, emphasis mine)
For when I have brought them into the land flowing with milk and honey, which I swore to give to their fathers, and they have eaten and are full and grown fat, they will turn to other gods and serve them, and despise me and break my covenant.
(Deuteronomium 31:20, emphasis mine)
Moreover, I swore to them in the wilderness that I would not bring them into the land that I had given them, a land flowing with milk and honey, the most glorious of all lands (...)
(Ezechiel 20:15, emphasis mine)
"Milk and honey" are usually seen as refering to the fertility of the soil, which is very important to an agranian society. Today, the phrase is often used with little or no biblical or religious context. It typically refers to a land where a person isn't at the moment, but they hope to get there one day. Once they get there, everything will be better, all the hardships and the scarcity will be over, there will be plenty for everybody. It's more a land one yearns for than an actual reality.
The concept is similar (but not identical) to Paradise or Cockaigne (also known as Schlaraffenland, Luilekkerland, Paese della Cuccagna).
But as we all know, there is no land where milk and honey flow, there is no place where everything is easy and there are no hardships or setbacks. And in your quote, the person described had to learn that too:
He never had a chance in the land of milk and honey.
meaning "he went to what he thought to be the land of milk and honey, but he never had a chance there (and subsequently didn't make it there)".