I am writing to seek possibilities of having a continuance for my hearing on 02/13/2014.
The sentence is probably grammatical, but it's awkward and the word choice is poor. What does it mean to "seek possibilities"? Oh, you'd get the meaning across, no problem, but it sounds odd.
Here's my advice: be bold and assertive. Do not seek possibilities, just come right out and say what you want. Try this:
"I am writing to request a continuance of my hearing on 2/13/2014." And then indicate the reasons why the continuance should be granted, and suggest a reasonable date for when you would actually be available.
By the way, in a matter of legal procedure you say a "continuance of", not a "continuance for". A "continuance" in US legalese is a word they use instead of "postponement", so the same preposition, "of" is what is used.
By the way, if you are actually trying to request a continuance in some case, check this out: