I’ts doable but there is few issues you need to overcome. For one you can use https://esi.tech.ccp.is/ui/#/Universe/get_universe_system_kills to get the number of kills per system in last hour, however that doesn’t tell you who was fighting or what was lost, or who won for that matter.
To get actual usable information like what ships were involved or who was involved you need to get killmails, this can either be via ESI from people/corps who logged in and granted you access to their killmails or from people manually pasting in the killmail link. There is no global killmail feed.
Unless you want to start gathering killmail ESI tokens from a vast majority of the game it would probably be easier to just consume zKill’s API and let it handle the processing and you just build a custom view, similar to what https://br.inyour.space/?s=2948&b=8052060&e=210&t=yKLG does.
This would actually be quite helpful if you could make something nice, especially with the new killmail format coming up next month. As both zKill and br.inyour.space will have to be updated to make use of the new data. Examples of that new format can be found here: https://github.com/ccpgames/esi-issues/tree/master/new_killmails