Shiny Groudon Rate

Would expect it is the same as any raid boss (or at least legendary raid boss).

Not sure on the exact number, but it's approximately 1 in 20-25 (or 4-5%) from what I've heard.

Although I've generally had more success than that:
0/6 articuno
1/11 zapdos
1/13 moltres
1/20 kyogre
1/7 groudon
1/13 ho-oh
0/6 Lugia

There's nothing official because Niantic doesn't make that information public. Based on controlled research odds are seen as 1 in 20, about the same for any shiny legendary.

I can only show my experience.

0/24 articuno
2/21 Zapdos
1/16 Moltres
0/14 Lugia
1/17 Ho-oh
0/24 Kyogre
0/19 Groudon

I believe it is 1/20 :)

I also believe it's the standard 1/20-ish odds.
I'll also share my numbers because I think they're quite funny:
1/7 articuno
0/0 zapdos
1/22 moltres
4/27 kyogre
0/12 groudon
0/21 lugia
0/5 ho-oh

Y'all are funny. I don't know my actual legendary raid breakdown, but I've done 67 legendary raids and gotten a big whopping 0 shiny legendaries. I got a shiny Zapdos from a research task once.