There is no direct conversion between these measurements because a milligram is a measure of mass and a teaspoon is a measure of volume. However, there are 0.00018 teaspoons in 1 milligram of salt, so 1 milligram divided by 0.00018 teaspoons equals about 5,555 milligrams per teaspoon of salt.
The teaspoon is defined in terms of fluid ounces, and equals 1/6 ounce. There are 14.3 grams in 3 teaspoons, or 4,767 milligrams per teaspoon for cooking purposes. The fluid ounce is based on the avoirdupois system, and equals the volume of 1 ounce of water in weight, but is defined in the United States as 1/128 gallon in volume.