Robin's pin cushion

Great fleas have little fleas upon their backs to bite 'em,

And little fleas have lesser fleas, and so ad infinitum.

And the great fleas themselves, in turn, have greater fleas to go on;

While these again have greater still, and greater still, and so on.     

 (Auguste De Morgan)

Is this a flower or a fungus or what?

Well if you look at the photo you can see that it is growing on the stem of a rose, which gives us the clue that it is a Robin's Pin Cushion or Bedeguar Gall.

It is caused by some chemical exudate from the larvae of a very small (4mm long) gall wasp.  This causes the gall to form as a home and a food source for the grubs, with no harm caused to the rose plant.  It usually occurs on wild roses.

The gall will contain several gall wasp larvae plus inquiline species, which are opportunist insects that also move in and make use of the shelter and food provided.  On top of that you can get parasites of both sets of grubs and then hyperparasites of those parasites.  It's a whole tower block of inhabitants.

Not fleas though.

'Robin' refers not to the bird but to Robin Goodfellow, 'the woodland sprite of English folklore' (wikipedia)