Are mp4 bit rates the same as Flash bytes per frame? I'm converting Flash movies to Mp4 (and webm) and having to learn lots about web video.  

The process starts with MOVs exported from Flash. For example, I have a MOV of 640px x 290px, 1m 58s, 2843 frames, 24fps, 171 MB, 11 Mbps. 

Converting that to H.264 with Handbrake, with constant quality of 20 RF, I get a file of 3.45MB with - according to MediaInfo - "overall bitrate mode: variable", and an "overall bitrate" of 240 kbps (video 79, audio 144 with max 170). Bitrate Viewer tells me the average bit rate (this might be video only) is 92 kbps, with a 1-second peak of 1019.     

Then I tried Handbrake's variable bit rate, because (if I've understood its advantages correctly) there are 20 seconds with lots of motion, in the middle of the video, which might look better with a higher bit rate. With VBR 300, I get a 6.3 MB file with (MediaInfo) an overall bit rate of 440 kbps, video 300, audio 144. Bitrate Viewer has average 293 kbps, with that peak now at 3467. For about 65% of the video it is below 130 kbps. I've placed the Bitrate Viewer profiles here: http://www.casedasole.it/bitrates.html

With Flash, bytes per frame were important because, when streaming, you needed to have the browser download as much as possible in advance, so that particularly big chunks of bytes (like a big JPEG) were already loaded before the Flash player reached them. 

My question is: Is that the same principle with video bit rates? Looking at that peak bitrate of 3467 (converts to 433 kB), I think: "That's OK, by then, the whole video will be loaded".  Or am I missing something?
Comparable yes but unlike Flash you have a very consistent average size over the timeline of your content. So you don't need to download as much to show content but can actually just start right away to play the video if your bandwidth is equal to (in practice it should be a bit higher of course) the average bitrate of your video. You only need to pre-load a tiny bit to account for inconsistency in the download rate.

Edit: What you have to consider when using looking at the graph you posted, you have quite a bit of very low bitrate frames, so the peak is not really that important, they somewhat cancel each other out. Whats important when streaming is the average bitrate as this is the bitrate that is needed to stream the video consistently without stopping to fill the buffer a bit more.
In reality you usually need a little more than the average to cope with very "noisy" bitrates that go up and down for long periods, your video is already a rather extreme example, usually you have a much smoother graph. It always depends on the complexity of your video to how well you can compress a frame.