There are two ways this could be done, one of which used to be popular (but has since been abandoned, because its basic premise has been refuted), and one of which is currently being done successfully (I'll point you toward a reading suggestion!).

One way to write a history of race struggle would be to treat race as an essential category, that is as something that is biologically real and which didn't change through time. This is how historians, anthropologists, and archaeologists often approached history in the 19th and early 20th century. The histories they produced stressed conflicts between migrating groups of biologically different, distinct people, and treated culture and ancestry as the same thing (so, if you were born a 'Goth' you died a 'Goth', and no one not born a Goth could become part of the Gothic tribe). Some of the more polemical strands of this scholarship warned of the dangers of race mixing, suggested Jewish conspiracies to destroy Aryan culture, and ultimately wound up being co-opted by (or evolving into) racializing ideologies like Nazism in the mid 20th century. The more benign versions still assumed that people who lived in different countries were fundamentally different kinds of people -- that race was real, unchanging, and rooted in the distant past.

After WWII, a lot of scholars questioned whether these approaches were valid / true, and 70 years of hard scientific and anthropological study has proven that they absolutely were not. Historians and anthropologists now recognize that 'racial' or 'ethnic' groups are socially constructed -- that is, membership in these groups depends on social factors, not biology. In America today, for example, being 'black' refers to a combination of skin color and cultural habits -- having an ancestor who was African American might not mean anything for your racial identity; but in the 19th century, skull shape could, for some race theorists, matter more than the color of your skin, while one-drop rules meant that any amount of African ancestry prevented one from being legally white. That is, what makes someone 'white' or 'black' changes over time. Biologists, for their part, have proven that there are no significant biological differences between 'races', that is: these groups are all in our heads, and recent studies of ancient DNA and migrations show that people in the past intermarried just like we do today -- 'race' isn't an objective category, isn't something societies invent in the moment to make sense of their contemporary circumstances, and it changes as these circumstances -- and these societies -- change.

This brings us to the second approach to race struggle, which I would argue is an important focus for historians today. This approach is to study race as a discourse, that is to study the way we imagine or talk about different groups of people, and how we then turn these imaginings into concrete historical and social realities (through individual actions, laws, etc). Who precisely fits into a 'race' has changed over time, so we can't merely study some sort of monolithic conflict between 'white' and 'black' over time (what being 'white' and 'black' means, in America, has shifted over time, and many other countries use other classifications for sorting humans into 'races'). We can, however, trace how the act of categorizing -- discourses or descriptions of race -- has changed over time, and the social consequences that result from centuries of people in power using the idea of 'racial' difference to exert power over / exploit other people. A great recent example of this kind of approach would be I. Kendi's book, Stamped from the Beginning (2016).