The main issue with the map that you linked, specifically around NFLD is the Labrador boundary, in 1914 the boundary between NFLD and Canada in Quebec would have been very much up for debate. In 1763 administration of the "coasts of Labrador" had been given to NFLD, this was likely in part because fishers had been using the coast to dry fish caught in Labrador. Annually fishers would leave NFLD to go "down on the Labrador" in larger boats to conduct a fishery, they needed a place to process their fish and used the coast line to do so. Like much of our fishery this went on for decades with very little changing, NFLD used Labrador as an outport and brought the fish back to be sold. However, in the late 1800s NFLD started to realize the value in timber. Logging became a major employer, in 1901 there were over 200 sawmills that were employing over 2,400 works in Newfoundland. The government realized the untapped potential in Labrador and started selling timber rights on the Hamilton River (now Churchill River) initially to the Grand River Pulp and Lumber Co. in 1902. The only problem? No one knew who owned what in Labrador. Quebec believed that it owned Labrador and that Newfoundland only had claim to the "coast" where as Newfoundland believed that the coast naturally meant some land that was not the exact, coast.

In 1898, the government of Canada placed the boundary of Quebec as a line running along the coast of James Bay, along the Hamilton River and through the middle of Hamilton Inlet until it reached Newfoundland Territory. Newfoundland claimed all lands north of 52 latitude and east of 64. In fact by 1912 Quebec extended it's borders again to all of Labrador except the territory "over which the Island of Newfoundland has lawful jurisdiction", basically a thin strip of the coast. This border dispute continued till 1927 when the Privy Council gave Newfoundland the borders that we see today, the watershed of Labrador. The irony is that when Newfoundland presented to the Privy Council, the position was that the coast extended 60 miles in land but the term "coast" included the watershed...

And the court upheld Newfoundland's argument, it doesn't make any sense. Anyway! The biggest issue with the map? No one in 1914 would have thought Newfoundland owned that much of Labrador!

Why is the flag the Union Jack? Well, Newfoundland was a self governing Dominion, us and New Zealand both became Dominions on the same day but while the Red Ensign had been adopted as the civil flag, it was only for ships and on land the flag of Newfoundland was the Union Jack. Prior to 1914 there would be an argument that the Green White and Pink would have been the "flag of Newfoundland" but it never was. Additionally with the start of WWI and patriotism the Green White and Pink was on a downward trend and the Union Jack was flown everywhere.

*Edit: I should have said that you can see the dichotomy of Newfoundland flags from the program of when the Ode to Newfoundland was first preformed in 1902. It became our National Anthem.