It seems that all Praat scripts operate on recordings. Is there any such thing as a script that performs an analysis "on the fly"?
I'm guessing by "on the fly" you mean you can be speaking into a microphone and seeing a waveform, spectrogram, pitch contour, etc. produced as you speak into the microphone? Praat cannot do this, but WaveSurfer (another free speech analysis program) can. You can decide ahead of time what types of display windows (called "panes" in WaveSurfer) to have open, and then as soon as you hit the record button all the displays start scrolling across in real time. As soon as you start speaking into the microphone, you can see the various panes responding accordingly. When you hit "stop", the scrolling stops and the displays become static and you can interact with them largely in the way that you would in Praat.
Praat is great for certain things, but WaveSurfer is great for demonstrations in classes when first introducing the concept of a spectrogram. It shows very quickly what different types of segments look like in a spectrogram, as well as the relationship between loudness and waveform amplitude, pitch and glottal pulse frequency, etc.