A database of the stroke orders for all of the Hangul syllables would contain a huge amount of redundant data. There are just 24 letters, but there are approx 11,000 different syllables that you can make with those letters (only 2,000-3,000 of which are actually used).
The number of the theoretically possible Modern Hangul syllables in Unicode is: 11,172. Among these, the top 2350 syllables occupy 99.9% of all that is used.
Initial consonant 19 * Middle vowel 21 * (Final consonant 27 + No final 1) = 11,172.
Among these, there are 3.192 possible syllable combinations possible in Korean phonotactics:
Initial consonant 19 * Middle vowel 21 * (Final consonant 7 + No final 1) = 3,192.
From Karavinka on the UniLang Language Community Forum
A database is not necessary. You can easily memorize the stroke order for 24 letters. This related answer has good information on the stroke order for those 24 letters: Hangul — printed vs handwritten
Since you're asking specifically about syllables, perhaps the missing piece of information is how to take those letters and compose them into syllables. How to Study Korean Unit 0 Lesson 1 has some good illustrations and explanations of this.