For a Hangul syllable chart it is best to google images for Korean
Alphabet and there are quite a few, some are coloured for teaching
children.

I also came across this article which is worth reading entirely, on
the classification of Hangul as an alphabetic or featural script.
However, it ends this way.


"Still， in attempting to evaluate a writing system， one very
important factor must be taken into consideration first． Most
critics， either Eastern or Western， have assumed the point of view
of the writer when evaluating writing and orthography． However，
this is a mistake． It is not fromm the point of view of the writer，
but of the reader， that a writing system must be judged． A work is
written by one，or at most， three or four people； but when printed，
that same work can be read by many thousands．

For this reason， I think the syllabic system (모아ì"°ê¸°) used in 한글
orthography is marvelously well adapted to the Korean language．
Because Korean is an agglutinative language in which particles and
suffixes are added one after the other to a stem， there are a very
large number of inflected forms， and in on-line writing (í'€ì–´ì"°ê¸°) it
can often be difficult even to distinguish where one inflectional
form ends and another begins． Grouping the letters into syllables is
an effective solution to this problem."

http://www.koreandb.net/sejong600/sejong03_231.htm

Suzanne McCarthy