The fickle storm is forecast to expire yet again after it crosses the islands and heads into the eastern Caribbean.
Kirk is moving toward the west-northwest near 16 miles per hour and this general motion with a slight decrease in forward speed is expected over the next few days.
Meanwhile, Kirk has restrengthened into a tropical storm, and tropical storm warnings and watches have been issued for portions of the Lesser Antilles.
Tropical Storm Kirk continues to move quickly toward the Lesser Antilles, where tropical-storm conditions are expected later Thursday.
"We don't believe Cayman will be impacted with the winds associated with Tropical Storm Kirk, but we do expect moisture", Mr. Miller said.
Kirk became a named storm Saturday and formed the farthest south of any major storm since 2012.More news: 49ers won't bring in Colin Kaepernick in QB search
Wind: Tropical storm conditions are expected to first reach the warning area by Thursday afternoon, making outside preparations hard or risky.
"This disturbance is likely to redevelop into a tropical cyclone during the next day or two before it moves into an area of highly unfavourable upper-level winds as it approaches the Caribbean Sea", NHC said.
A Hurricane Watch is issued when sustained winds of 74 miles per hour or higher are POSSIBLE within the specified area of the Watch.
On Tuesday, Tropical Storm Rosa formed off the Pacific Coast.
But, a sea advisory has been issued for the territory and the DDM said the advisory can increase to a "Warning" as Kirk gets closer on Friday.
RAINFALL: Kirk is expected to produce total rainfall of 4 to 6 inches across the northern Windward and southern Leeward Islands with isolated maximum totals up to 10 inches across Martinique and Dominica.