No, Jeanne, it’s not grammatically correct to state the term for a unit of measure in its plural form when it is being defined. In your first example, in particular, the grammatically correct way is to state the term in its singular form followed by the definition, as follows: “The inch is the smallest measurement of length in the British System.” The same grammatical pattern needs to be observed when defining all the other units of measure you enumerated: “The mile is…”, “The second is…”, “The year is…”, “The ounce is…”, and “The ton is…” All units of measure are notionally singular and need to be treated as grammatically singular as well to ensure subject-verb agreement. When modified by a specific quantity, however, a unit of measure is stated in the singular when the quantity is 1 or less than 1, as in “1 second” and “0.5 second”; then in the plural for quantities of 2 or more, as in “2 seconds” and “55 seconds.”
The conventional way to write “5,280” is, of course, to put a comma after the first digit as shown here. This follows the standard system of writing numbers in the thousands or multiples of thousands, where a comma is placed after the first digit up to a maximum of three digits, then by a comma after every three digits thereafter, as in “1,532,630” and “999,382,567,000.” As we know, however, those commas need to be dropped for calculation purposes using digital computers; this is because digital computers can’t do their computation routines with those commas present. Also, some scientific publications have adopted a style that dispenses with commas in numbers altogether. Both styles—the one using commas and the the other dispensing with the commas—are acceptable.