I also played with Flutter recently. Timeline: heard Kotlin announcement at I/O, went through some Kotlin exercises, wanted to compare with Flutter/Dart.
Dart feels somewhere in between JavaScript on the one hand and a more-static OO, GC'd lang w/type inference (like Kotlin!) on the other. You can probably look closely at some sample app code and start doing some basic stuff quickly if you've worked much with JS and something more static. (Further study seems worth it if you plan to do a lot, heh!)
As others note the UI model seems Reacty--you write "builder" methods that recreate a widget tree when things change, and something behind the scenes sorts out an efficient way to update the screen with just what really changed. I'm not hugely worried about performance: your UI rebuilds should be separated from your animations, and anyway, building your virtual widget hierarchy ideally shouldn't be too CPU intensive in the first place.
Hot reload is pretty great. I can't actually compare with "real Android" dev, but changes to my little app showed up in under a second in an Android phone, emulated or real. There were a couple surprising things about the basic libs, e.g. Flutter master only recently added a convenience object to bundle together a radio/checkbox and its associated label-stuff (RadioListTile).
The Flutter Gallery app is available on Google Play and its source is in the Flutter git tree. You can see a lot of the Material widgets implemented, including rich list types (e.g. tiles w/photos), pull-from-the-side drawers, top-of-screen tabs you can swipe through, bottom-of-the-screen nav bars etc. Even on iOS Google seems to follow Material guidelines a lot (or at least, the Daring Fireball guy complained that they do; I don't have iOS to check), so maybe it's the easiest fit if you're prepared to do the same. Someone who works on Flutter mentioned elsewhere in these comments that they're working on components that look more like the iOS-native ones, though.
Although Android Studio is _based on_ IntelliJ, you need to get actual IntelliJ if you want to use the plugin (Studio's component versions don't match the ones that the Flutter plugin works with, I think). Also, if you have Studio 3.0 canary installed (like to futz w/Kotlin, heh!), you need to either configure Flutter to look for the stable Studio 2.3's copy of Gradle (flutter config --gradle-dir=...) or just make sure 2.3 is located where the flutter tools look by default (~/android-studio for me on Linux). People working on Flutter helped some of us through this at https://github.com/flutter/flutter/issues/10236#issuecomment...
You get a lot of IDE-ish luxuries (as OP notes): Control-Space to offer identifiers, methods, or params available; autoformatting with dartfmt (right-click menu); lots of quick feedback when you mess something up.
Hixie (Ian Hickson) of the HTML5 spec works on Flutter which is kinda neat (he did RadioListTile just now! and there's a milestone on GitHub named 'Make Hixie Proud' haha :D). Outside of the tech specifics, Dart's an interesting creature in that it seems like it's got some key customers in Google (AdWords, so, like, the part that makes money) but comparatively little pickup outside. On Flutter GitHub you see people paying attention to outside-adopter issues (or even passerby issues such as my Gradle-version thing recently). There's apparently lots of tooling available publicly, e.g. a package manager (pub), dartfmt, IDE plugins, a playground (dartpad.dartlang.org) etc. Curious to see if there's any more pickup on the outside.