I don't know Dutch, Flemish, or Afrikaans, but will sometimes, on coming across a writing sample of one of them, wish to know which it is. How do I distinguish them in their written forms?
Written texts in Flanders, such as newspaper articles, are so close to standard Dutch that you are unlikely to be able to distinguish them except by context.
Afrikaans is different and the more Dutch you learn the easier it is. An instant clue is the use of -y- (e.g. instead of -ij-). The use of 'n instead of een as the indefinite article and die instead of de as a definite article will also stand out, as does the very different spellings of pronouns. And then it goes on.
In the case of Afrikaans, the two most salient features would be the spelling (as has been pointed out by Henry) and Afrikaans' double negation, which is absent from both Dutch and Flemish.
If you see a text peppered with "die", "'n", "hierdie", "daardie/daai" (determiners) or "hy", "sy", "my", "julle", "hulle" (personal pronouns), "is" (copula: present tense), "was" (copula: past tense), you're probably looking at Afrikaans.
Negation can be spotted in the form of the words "nie", "niks" and "geen" closely followed by a second "nie".
For details, check out this Wikipedia entry.