Correct spelling for the English word "draggest" is [dɹˈaɡəst], [dɹˈaɡəst], [d_ɹ_ˈa_ɡ_ə_s_t] (IPA phonetic alphabet).
I’m sorry, but there doesn't appear to be any information available regarding the etymology of the word "draggest". It doesn't seem to be recognized as a standard word in English. It's possible that it is a misspelling or a regional variation of another word.