Unless there is a particular reason why you need the text in separate autosized frames, then you should be using paragraph styles with space after to achieve what show in your screenshot.
that can be done, if you really need it.
For InDesign CS6 and above the trick is:
1. You need a inset space at the bottom of your text frame, that is giving you the distance to the text in the next frame.
2. You have to stack all text frames in one "column" and align them to the top of the column
3. On every text frame have a text wrap
Here a screenshot from my German inDesign CC 2014.2:
Have the Layers Panel open to adjust the stacking order of your text frames.
That's very clever.
Thank you Laubender!!!!
You have saved me and my team hundreds of hours and taught me something I will use ALL THE TIME.
Mögen all deine Träume und Wünsche in Erfüllung gehen!
but I don't think you should use this technique "all the time".
Just in special use cases.
Usually separating text portions by paragraph returns and space before, space after is recommended.
But, of course, there are good cases.
One example (just out of my head):
Every textframe is one logical unit, a single building block of text, that is linked to an distinct text file, that could be updated easily.
Oh noes, now I'm questioning everything. This file is updated frequently via data merge and I assumed it would be wise to have separate fields instead of one. Based on your and smoothsea's responses that may not be true.
Is this document considered a template for a data merge process?
Then go ahead, do some testing and report back here how it goes.
I'm really interested in your use case.