Where can I find my K/D and kill-streak stats in Battlefield 1?

It looks like you can only view it online, not in-game. See here:

You can access the current test version at the following address. (EA login required)

https://www.battlefield.com/companion/career

You can view your stats from BF1 and BF4, see your kills per weapon/vehicle, edit your infantry/vehicle loadouts and check your progress on medal assignments.

You can also go to BF1Stats.com

I've been using this site for years. It helps with tracking unlockables, rank, scores, etc. Very in depth site.

Now keep in mind I don't play very much of BF1, but I have been using this site since BF3. At the top of the page where it says "P-Stats Network", you can switch games and look at those too. Honestly, this site is much better than anything EA can put out. The only things it can't do is change your loadouts, skins, and choose a server. If you're looking for straight stats and stats only, this is the site you go it.