Short animations streamed on Kyoto Animation's YouTube channel in the lead up to the July 7 premiere of the second season. 
 
(Source: Crunchyroll) 
 
Note: This entry's total count includes episodes 1-13 + the 3 SP episodes that released during the second season's run.

Episode 1 - The Strongest Maid in History, Tohru! (Well, She is a Dragon)

Episode 2 - Second Dragon, Kanna! (We're Totally Spoiling Here)

Episode 3 - Start of a New Life! (That Doesn't Go Well, Of Course)

Episode 4 - Kanna Goes to School! (Not that she needs to.)

Episode 5 - Tohru's Real World Lessons! (She thinks she understands it already.)

Episode 6 - Home Visit! (And Homes Not Visited)

Episode 7 - Summer's Staples! (The Fanservice Episode, Frankly)

Episode 8 - New Dragon, Elma! (She's Finally Appearing, Huh?)

Episode 9 - Sports Festival! (There's No Twist Or Anything)

Episode 10 - Troupe Dragon, On Stage! (They Had A Troupe Name, Huh)

Episode 11 - Year End, New Year! (No Comiket Bit This Time)

Episode 12 - Tohru and Kobayashi's Impactful Meeting! (We're Raising the Bar on Ourselves)

Episode 13 - Emperor of Demise Arrives! (It Was the Final Episode Before We Knew It)

Kyoto Animation

Miss Kobayashi's Dragon Maid S: Miniature Dragon