In a medium-sized saucepan, add cubed potatoes and water to just cover the potatoes. Bring to a boil over high heat. Cover, lower heat to medium-high, and maintain a high simmer for about 15-20 minutes or until fork-tender.
Drain the potatoes and place in a large mixing bowl. Mash the potatoes until smooth with a pinch of salt and freshly ground black pepper.
Remove the casing from the sausage. Brown the sausage in a small non-stick skillet over medium-high heat. With a slotted spoon, scoop the sausage and add to the potatoes.
Before you add the chopped kimchi, take a paper towel and give the kimchi a gentle squeeze or pat to remove excess liquid. Finally, add the kimchi to the potatoes. An important note on the kimchi - use kimchi that is really tangy which means kimchi that has been around for a few weeks...refrigerated, of course.
Fold in the eggs and flour. Mix to combine the mixture evenly.
Heat a few tablespoons of oil in a large non-stick skillet over medium-high heat. Spoon about a 1/4 cup of the potato mixture while gently flattening it. Cook both sides until golden brown, about 2 minutes each side. Drain excess oil on paper towels. Work in batches.
Serve as-is or with a dollop of sour cream.