I have had some Rhino 380gr I want to try in my 375HH, but I need some data for it.
This have proberly been posted here before sometime, but I am not able to find it.
In fact, I have been looking for data all over the net today and found little and nothing.

Try mailing Norma
Norma

I googled "380 grain rhino" and there seems to be lots!

I have .375 Wby data and loads. Basically you need some fresh W760 and start out at 70 grains or so. The problem with lots of powders is getting enough in the case to get any speed up. 2400 fps is tops for me and I tried, at Mauritz Coetzee's suggestion, IMR 4350 with only 2200 fps or so. [W is Winchester powder, not VV as in Vihtavouri.]

Keep in mind how LONG the bullets are. Surprisingly the 350's are even longer!! Barnes data might be your friend (or SWIFT, Accubond, etc.) To be clear my .375 Weatherby load is 75 grains W 760 and I have found max H&H loads are a good starting point for mine, hence the 70 grains starting load I suggest.

I have a 350-grain Woodleigh load based on IMR 4831 -- a much shorter based bullet that allows me 81 grains crimped @ cannelure. You could try 75 grains as a start there, but I bet it won't fit magazine length/.375 H&H chamber.