It's not that you'd be misunderstood. German listeners are thrilled when you try. It's just a question of emphasis. The polite way to say you don't care for vegetables is "mag kein". To say "Ich mag [whatever] nicht," is sort of like screaming the "nicht." A toddler or a dictator would say, "Ich will Gemüse nicht!" There is a lot of play in the language, but some formulas are softer and gentler.
My understanding is the following, but I'd welcome confirmation, correction or additions from a native speaker or more advanced student:
We use nicht when ...
We are negating specifically the verb - Ich gehe nicht
The noun has a definite article - Ich mag das Gemüse nicht
The noun has a possessive pronoun - Ich mag dein Gemüse nicht
It's a proper noun in the sentence - Ich heiße nicht Veganpanda
We are negating an adjective used with part of sein - Das Gemüse ist nicht weißes
We are negating an adverb - Wir lernen nicht langsam
(But I'm not at all sure I have the rules right for where to put nicht in the sentence.)
We use kein when...
the noun would have an indefinite article if it weren't negated - Es ist kein Gemüse
The noun has no article or possessive pronoun - Ich mag kein Gemüse
Technically it's not proper English grammar. http://www.engvid.com/how-to-use-no-not-in-english/
The articles (der die das = the, ein eine ein = a, and a few others such as kein(e)) change to signal/agree-with the case and the gender of the noun they belong to.
Indefinite articles, kein:
Nom (m) kein / (nt) kein / (f) keine / (pl) keine
Akk (m) keinen / (nt) kein / (f) keine / (pl) keine
Dat (m) keinem / (nt) keinem / (f) keiner / (pl) keinen
Gen (m) keines / (nt) keines / (f) keiner / (pl) keiner
Table adapted from: http://german.about.com/od/grammar/fl/The-Four-German-Noun-Cases.htm
Here, kein is to be used in the accusative case with the neuter gender, so gets no extra ending. The ending with -s, keines is for the genitive case, for masculine and neuter genders.
If there are any mistakes in the above, let me know on my profile and I'll correct them here. Thanks.
I wrote "I don't like vegetable" and it is falsch. Why?
Because "vegetable", in English, is a countable noun; it's usually used in the plural, as "vegetables".
The German noun Gemüse, on the other hand, is almost always used uncountably.
So Gemüse (mass noun, singular) usually translates best to "vegetables" (countable noun, plural).