North Korean dictionary order

JavaScript (ES6),  150 148  137 bytes

Saved 10 bytes thanks to @Grimy

I/O: arrays of characters.

a=>a.map(c=>"ANBCODEFPGQSHRIJKLM"[(n=c.charCodeAt()-44032)/588|0]+"AKBLCMDNERTOFGSUPHIQJ"[n/28%21|0]+~(n%28%18==2)+c).sort().map(s=>s[4])

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Splitting Hangul syllables

Given a Hangul character of code point 0xAC00 + \$n\$, the initial consonant \$I\$, vowel \$V\$ and final consonant \$F\$ are given by:

$$I=\left\lfloor\frac{n}{588}\right\rfloor,\ V=\left\lfloor\frac{n}{28}\right\rfloor\bmod 21,\ F=n\bmod 28$$

Commented

a => a.map(c =>                  // for each character c in the input:
  "ANBCODEFPGQSHRIJKLM"[         //   start with a letter from 'A' to 'S'
    (n = c.charCodeAt() - 44032) //   for the initial consonant
    / 588 | 0                    //
  ] +                            //
  "AKBLCMDNERTOFGSUPHIQJ"[       //   append a letter from 'A' to 'U'
    n / 28 % 21 | 0              //   for the vowel
  ] +                            //
  ~(                             //   append "-2" for ㄲ or ㅆ (the only North
    n % 28 % 18 == 2             //   Korean final consonants that are sorted
  ) +                            //   differently) or "-1" otherwise
  c                              //   append the original character
)                                // end of map()
.sort()                          // sort in lexicographical order
.map(s => s[4])                  // isolate the original characters