Use drinkt when the King James Bible would use drinketh, which in today's English has become drinks.
In most cases you should also use drinkt when the King James Bible would use drinkest, which in today's English is just drink because the second person singular was replaced by the second person plural for politeness.
Dutch is not derived from English or German. If anything, you could say it was once a family of German dialects that were closer to English than most of the others, and created a competing standard when the German language was standardised. In a bit more detail:
Dutch, English and German are very closely connected as the three major West Germanic languages. The others are Yiddish and (East and West) Frisian. Also Scots, Swiss German and other little languages that can also be considered dialects.
English has extremely strong connections to what the Angles and Saxons once spoke (hence "Anglo-Saxon"). The Angles lived a bit north of Hamburg, near today's border between Denmark and Germany. The settlement area of the Saxons included what is today the Netherlands. So there was a strong linguistic connection, and it was held alive by interactions over the centuries between the two sea-faring neighbour populations. (E.g., Dutch engineers shaped much of the English landscape. Many English cities such as Ely were islands before these engineers set to work.)
Until about Martin Luther's time, there wasn't really a standard German language but a large dialect continuum that included Dutch. But at the time, German was standardised (in part because the farmers started reading religious treatises printed cheaply using Gutenberg's relatively recent printing presses!) and the Dutch speakers decided they didn't like the new standard, translated books written in the new standard into their own local dialects, and gradually created their own standard language.
You can find more about that in Wikipedia: https://en.wikipedia.org/wiki/West_Germanic_languages West Germanic languages map: https://upload.wikimedia.org/wikipedia/commons/0/07/Lenguas_germ%C3%A1nicas.PNG