The flower with only three letters in its name is the "lily."
Ivy
pansy
ham
poppy, daisy? poppy, daisy?
the only flower mentioned by name is Primrose.
A gazelle is a type of antelope.
Bang, boom and snap have 4 letters.
eft
Try HEN
Waiting for you (three words)
A flower is a flower. A tree is a tree. There different in spelling and the number of letters.
If I understand the "rule of seven" that you are looking for, it applies only to capital letters, not to "small" letters. When the small letters are written out as they appear in script rather than in type, then e, f, g, j , k, and l meet the conditions as do the three that are not in your list. (Even in type, e and g are in the group.) Think "geometry."