Who were the gym masters of the time? What was the nature of the culture how uniform was teaching? Where dark skinned fighters even taught in a gym? A lot of greats from the earliest eras seemingly were self taught and learnt on the road from one another in sparring and perhaps passing lessons between friends from them our styles today are the progenitor of, every clever jab a tribute to our sports heritage in Corbett. Our styles today even in the most shallow fundamental form are the fruit of hundreds of years of fighting what is often unknown to the young scrapper is that he has inherited a champions arsenal.
You may be surprised to hear that is was the Welsh who had a big influence on the way Boxing training was developed, adapted and tested towards the scientific MoQ style we know today. The famous 'mountain fighter' Dai Dollings, for example, was the one who taught Ray Arcel everything he knew about training as a young man. Arcel hung on his every word. Boxing booths were also instrumental on the development of the British style. Read my thread for some info on this subject: https://www.boxingforum24.com/threads/jimmy-wilde-dai-dollings-and-welsh-mountain-fighting.648053/ As for Boxing 'gyms' themselves, they have been around for a long, long time, since the days of Broughton, Belcher and before. And yes, some coloured fighters did get schooled. For more info on this subject, look through @BitPlayerVesti and @GlaukosTheHammer threads from a few years back. It is actually my personal opinion that the bareknuckle days of the late 1700s to around the 1850s was actually more 'skilled' (since Boxing was basically a different sport back then, which fighters had fully adapted to for over a century at the least) than the early 1900s, although this is much more prominent in the HW division than any other IMO (since big men are rarer and also uncoordinated).
There was actually a lot of amateur boxing in that period, California seems to have been especially prominent for early amateurs. Joe Walcott had fought as an amateur for example (both as a boxer and wrestler), so it was certainly open to black fighters.
There were loads of boxing gyms back in those days. Here in London they were often located above or behind pubs. The pubs were usually run by retired boxers.