I wonder whether it is correct to write “with all good wishes of health and happiness”? Is it ok to use the preposition “of” here. Thanks in advance for your help.
The language is a little florid, and it would be more natural to use for rather than of, but it's otherwise fine.
When people wish, and the aim of that wish is a noun, the usual phrasing is that they wish for that thing. If they are wishing with the aim of something being done, a verb phrase, it's usually wish that ("I wish that I were ten feet tall", or "I wish that you had a heart"), though you can also omit any preposition in that case ("I wish you would just stop fighting").
However, "wish of" is also attested, often for abstract nouns (like peace or love, or happiness). "Wish for" is significantly more typical, though. To see summary data on this, and you can try playing with other phrases, see this Google ngram.