The only real game programming I've done is with iOS and objective C. I'm switching to Android Game Development now. I've heard high praises for Libgdx, and Kotlin sounds like a nice language. But should I learn the traditional Java language for Android Development first, or can I start fresh with Kotlin and be fine in that regard?

You can do either.  The tools are free, so download them, look them over, read their web sites and tutorials and forums. 

Usually each new thing increases the learning curve.  You're moving to Android devices, you're using a new library, and you're using a new language you'll need to integrate with the Android functions (if they didn't do that already, I don't know). 

It is a sharp learning curve so don't expect your first few projects to go well.  It may be too sharp of a learning curve for your, or may not.

Up to you, I'd say. I've been meaning to try Kotlin for a while now. For someone who has been studying Java quite a bit, the features that Kotlin provides on top of Java are quite appealing, such as the feature of enforcing non-null references by default (I've just been too lazy to actually try Kotlin, but it looks really awesome).

But yeah, maybe learning both LibGDX and Kotlin at the same time could be overwhelming. What you want to do is game development, which Kotlin doesn't help you with explicitly. In my opinion the best approach would be to become accustomed to native Java first working in LibGDX, understand its flow and limitations, then look at what Kotlin can bring to the table. At most I think Kotlin will save you time when you can see where it can improve over Java but it might just be a timesink for starting out. Should look into it sometime though, I reckon.

Thx for the input guys. I'm taking this class on Kotlin and Libgdx on Udemy. So far Kotlin seems nice, but I'm a bit worried that there will be a scarce amount of tutorials for it compared to Java (should have realized that before taking the class). That's probably the biggest downside for me. Oh well. If all else fails I'll just go to Java. 

Edit

I'm switching to Java and Android Studio. It's best to learn the basics of Android App Development first. Gotta crawl before I can walk