I think after 10 chapters it's time to for a first review, keep in mind that a lot might change and I will probably edit this review in the future.
With Dragons Rioting we have somewhat of a highschool action shounen and my guess is it will turn into a harem, probably including a little bit of romance (or at least I hope so)

Story: 7
Well, we have a school full of beautiful girls that kick serious ass. So far as we know the school is ruled by the 3 dragons, especially strong girls who gained a huge fellowship in the school.
Our MC Rintaro appears and more or less accidently makes a big entrance which causes one of the dragons to ask him to be his apprentice, but because of his extreme condition he is reluctant.
From there different girls show themselves, all of them incredibly fighters. Around chapter 7 there seems to be developing an interesting plot, that I won't mention here.

Art: 9
The art is really amazing, it's sharp, clean and every character looks great, but while the characters look awesome, the backgrounds often fall a little bit short, though this is only a minor issue which doesn't really influence my view on the manga.

Characters: 7
The MC Rintaro seems like a mix between Kinjirou Sakamachi (Mayo Chiki!) and Yoichi Karasuma (Asu no Yoichi!), extreme gynophobia due to his medical condition and an incredible strong fighter, very likeable and room for development, which I'm looking forward to
The girls so far kind of lack depth, you have the airhead, the strategist, the kickass and a buch of other different types, all of them beautiful, although I hope they will get some more development (there were allready hints to that, so I'm sure this point will soon get raised to 8)
The only other male characters so far are in a supporting role, you have Rintaros father who trained him and his two friends from school which serve pretty much only as commic relief but do a good job at that

Enjoyment: 9
Switch off your brain and enjoy, the premise might seem stupid, but it's just a blast to read this manga, you have really hilarious moments, as well as great action scenes, it's simply light hearted fun and so I impatiently wait for more chapters

Overall: 8
So for we have a very good action manga with a lot of very well drawn ecchi scenes and fan service, but hey, it's that kind of manga, so what did you expect?
It's very promising and I'm really looking forward to where the Author is going with this one.
Of course it's still early into this manga, but so far I can give an absolute recommendation if you like this sort of thing! For everyone else (except maybe hardcore shoujo only fans) it's still worth a try.