"He drinks from the bottle."
Translation:Er trinkt aus der Flasche.
Just to add to what Lenkvist said... this will help you in the future:
"vom flasche" is not correct in any context.
"vom" is short for "von dem", masculine ou neuter dative.
"von" always takes the dative, "Flasche" with a capital F, is féminine. So you need "von der Flasche". However this only seems to be used in the sense of "off the bottle", ie taking a capsule off the bottle or weaning a baby off the bottle, as opposed to drinking something out of the bottle.
It's how the article die declines:
die - nominative
die - accusative
der - dative
der - genitive
aus is one of those prepositions that require the dative, so die declines to der.