Asia
The Gulf Stream is a warm ocean current that flows from the Gulf of Mexico along the eastern coast of North America towards Europe. It helps maintain Europe's relatively mild climate by bringing warm water and air to the region. The Gulf Stream also influences weather patterns and can impact precipitation and temperature in areas it flows through.
Google maps indicates that the distance is about 821.137 miles. It's the wildest water on earth, based on the volume of water that flows through it, and it's named Drake Passage. Read more about Drake Passage, below.
The Danube River flows through southern Germany.
The Amazon River is located in South America. It is the second-longest river in the world and flows through several countries including Peru, Brazil, and Colombia.
South America The Falkland Current is a cold ocean current that flows along the southeast coast of South America.
South America.
South America
The "Circumpolar Current" is the longest ocean current in the world and flows in an easterly direction.
Antarctic
Ninety-eight percent of Antarctica is covered by an ice sheet, meaning it is not known for its rivers. Any flowing water on the continent is seasonal glacial melt. The Onyx is the largest of these. The water from it that does not evaporate, flows into Lake Vanda, which is also frozen.
The North American coast
You may be thinking of the circumpolar current in the Southern Ocean.
Since 98% of Antarctica is covered with an ice sheet, it is not known for its rivers. However, seasonal, glacial melt-water rivers do exist, the most notable of which is named the Onyx River, which flows into Lake Vanda. Note that none of the melt-water flows into the sea, but eventually evaporates as it flows away from the glaciers.
South Alantuc Ocean
The Mississippi River flows on North America.
Antarctica is not known for its rivers, because as you assume in your question, the continent is covered -- 98% of it -- with an ice sheet. Any 'river' in Antarctica is truly seasonal, glacial melt water that flows in the 24/7 summer sun. As it gets colder, the water freezes again, the glaciers freeze again, and there is no more 'river.'