Even the Merriam-Webster dictionary acknowledges both ducky and jake as acceptable terms meaning fine or satisfactory and it dates the word ducky back to 1897 and jake to 1914. Does anyone know how either of these words--ducky or jake--came to mean fine or satisfactory?
Etymonline offers very little information on these words:
ducky — "excellent," slang from 1897 (often ironical), perhaps from duckie as a term of endearment (early 19c.). Probably not related to much earlier slang noun meaning "a woman's breast" ["...whose pritty duckys I trust shortly to kysse," Henry VIII, c.1536 letter to Anne Boleyn, who, contrary to rumor, did not have three of them].
"Ducky" has more modern synonyms in "peachy" and "hunky-dory":
Everything's just peachy.
(Note: Matt's comment about BrE usage seems to match the term of endearment mentioned as a possible origin.)
jake — Slang meaning "excellent, fine" is from 1914, American English, of unknown origin.
I've not actually heard "jake" used in this manner.
Sadly, there doesn't seem to be much other information easily available. The etymology of specific words is not always fully understood.
colloquial or familiar abbreviation of the masc. proper name Jacob (q.v.). As the typical name of a rustic lout, from 1854. (Jakey still is the typical name for "an Amishman" among the non-Amish of Pennsylvania Dutch country). Slang meaning "excellent, fine" is from 1914, American English, of unknown origin.