Python, 338 bytes

from textwrap import*
s,I,C,S,N='YAML:\nIt\'s "kek".',indent,':',' ','\n'
t=s.replace(C,C+N)
print('\n'.join(map(lambda x:'-'+I(x,S),[s.replace(C,'.\n'),"'"+t.replace("'","''")+"'",'"'+t.replace('"','\\"')+'"']+[p+(str(n)if n else'')+"\n"+I(t if '>'in p else s,S*(n-1 if n else 4))for p in ">:|:>+:>-:|+:|-".split(C)for n in range(10)])))

Attempt This Online!

This produces the following JSON output when pasted into "Online YAML parser"

[
  "YAML.\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".\n", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\".", 
  "YAML:\nIt's \"kek\"."
]

Before I try to get creative with more golfy techniques: is this the correct result? I still am not sure exactly whether or not I could get rid of the trailing newlines for some of these "indentation indicators". I am sure their creators meant well, but this is Perl-esque syntax madnes....