Unfortunately, Black Ops 4 doesn't have as complete a combat record as previous titles, but you can use a simple website to view all of your stats in full.
Because Black Ops 4 multiplayer is now more focused on 'EKIA' (which includes assists) rather than straightforward kills, you can't actually see your K/D ration in game, rather only your EKIA ratio.
Website 'COD Tracker' will allow to not only see your K/D, but so much more, including Total Damage, Damage per game, Heals per life, Average time alive per life, Captures and Defends, to name a few.
Simply enter your PSN Online ID, Xbox Live username or Battle.net name and search.
In addition to general and career stats, you can also see specific weapon stats, split into class categories like SMG, AR and so on.
You can also view the wins and losses from entire match history, separated per day, plus kills and deaths in those games.
There are also specific statistics for every specialist weapon and special issue equipment, plus accuracy and EKIA ratio for specific weapons.
There are also multiplayer leaderboards, which are not yet available in game officially (although Treyarch have said they will be available one week after launch).
So, if you want to see where you rank on the Kills, K/D ration or even deaths leaderboard, you can find them here:
Unfortunately, at the time of writing, Blackout statistics are not yet available, but COD Tracker says they are coming soon.
So, you might want to bookmark this page and check back regularly to see your battle royale.