According to Wikipedia:
Ka
Kachess River - Washington
Kakagon River - Wisconsin
Kakhonak River - Alaska
Kalama River - Washington
Kalamazoo River - Michigan
Kanab Creek - Arizona
Kanawha River - West Virginia
Kanektok River - Alaska
Kankakee River - Indiana, Illinois
Kansas River - Kansas
Kantishna River - Alaska
Karluk River - Alaska
Kasilof River - Alaska
Kaskaskia River - Illinois
Kaukonahua River - Hawaii
Kaweah River - California
Kayaderosseras Creek - New York
Ke
Kellys Creek - West Virginia
Kenai River - Alaska
Kenduskeag Stream - Maine
Kennebec River - Maine
Kennebunk River - Maine
Kentucky River - Kentucky
Keowee River - South Carolina
Kern River - California
Kettle River - Minnesota, tributary of St. Croix River
Kettle River - Minnesota, tributary of Blueberry River
Kettle River - Washington
Kewaunee River - Wisconsin
Keya Paha River - South Dakota, Nebraska
Ki
Kiamichi River - Oklahoma
Kickamuit River - Massachusetts, Rhode Island
Kickapoo River - Wisconsin
Kilchis River - Oregon
Killbuck Creek - Ohio
Killik River - Alaska
Killsnake River - Wisconsin
Kinchafoonee Creek - Georgia
King Salmon River (Admiralty Island) - Alaska
King Salmon River (Egegik River) - Alaska
King Salmon River (Nushagak River) - Alaska
King Salmon River (Ugashik River) - Alaska
Kings River - California
Kings River - Nevada
Kinnickinnic River - Wisconsin (Lake Michigan tributary)
Kinnickinnic River - Wisconsin (St. Croix River tributary)
Kinzua Creek - Pennsylvania
Kishwaukee River - Illinois
Kiskiminetas River - Pennsylvania
Kissimmee River - Florida
Kivalina River - Alaska
Kiwalik River - Alaska
Kl - Kn
Klamath River - Oregon, California
Klaskanine River - Oregon
Klehini River - Alaska
Klickitat River - Washington
Klutina River - Alaska
Knife River - Minnesota
Knife River - North Dakota
Knik River - Alaska
Knox River - New Hampshire
Ko
Kobuk River - Alaska
Kohlsville River - Wisconsin
Kokolik River - Alaska
Kokosing River - Ohio
Kongakut River - Alaska
Konkapot River - Massachusetts, Connecticut
Kootenai River - Montana
Koyuk River - Alaska
Koyukuk River - Alaska
Ku - Ky
Kugruk River - Alaska
Kuk River - Alaska
Kukpowruk River - Alaska
Kukpuk River - Alaska
Kuparuk River - Alaska
Kuskokwim River - Alaska
Kuzitrin River - Alaska
Kvichak River - Alaska
Kyte River - Illinois