Grammatically, when it comes to auxiliary verbs (auxiliary + verb), adverbs of frequency s.a. "never" should come after the auxiliary, in this case "will": will+ never+ do, i.e. will never do.
There is exception however for negative frequency adverbs s.a. the one mentioned. It is called "Style- inversion" where adverb and subject exchange places: Never will I [...]. This is applied for emphasis purposes and usually in literary works.
Any variants from these structures are grammatically incorrect.
결코 really means "decidedly".
But as it is used only in a negative context, it is ambiguously interpreted as "never" as in "(not) ... ever" in English.
In other words, 결코 prompts listener that a negative sentence is at play. 결코 itself is not a negative word as such.
나는 결코 그렇게 못 합니다
= I decidedly cannot do as such
= I can not do as such ever
= I can never do as such
There is no double negation involved.
Negative adverbs by implication are not negative adverbs in meaning.
This kind of "reserved/sole usage" of certain adverbs in negative sentences is frequent in Korean.
Double negatives on the other hand do exist in Korean but not in the sense of the use of "don't do nothing" to mean "don't do anything" (influence of latin-based languages?)
나는 여자친구가 없지는 없진 않아요 = I do not not-have a girlfriend
=> I have a girlfriend but it is as good as not having one.
This is not exactly the same as
나는 여자친구가 있어요. I have a girl friend (i.e. if the 2 negations cancel each other out)
The best you can interpret this adverb 결코, is "at any time; ever; at all".
But because it is used only in negative sentences*, it tends to be described as "at no time; never; not at all".
*negative sentences are those ending in 아니다; 안 / -지 않다; 못 / -지 못하다
결코 is used as an "amplifier" to emphasize and intensify the tone of the sentence.
• 나는 결코 그렇게 못 합니다.
못 합니다 = can not do
그렇게 = as such
결코 = ever
나 = I
= I cannot do as such ever
=> I can never do as such (/that)