A square pyramidal structure has five bonds and one lone pair, making a total of six electron pairs around the central atom. The geometry of such a molecule can be analyzed using the VSEPR theory.

1. $\mathrm{PF}_{5}$: 5 bond pairs and 0 lone pairs, so its geometry is trigonal bipyramidal, not square pyramidal.


2. $\mathrm{BrF}_{4}^{-}$: 4 bond pairs and 2 lone pairs, so its geometry is square planar, not square pyramidal.


3. $\mathrm{IF}_{5}$: 5 bond pairs and 1 lone pair, so its geometry is square pyramidal.


4. $\mathrm{BrF}_{5}$: 5 bond pairs and 1 lone pair, so its geometry is square pyramidal.


5. $\mathrm{XeOF}_{4}$: 5 bond pairs and 1 lone pair, so its geometry is square pyramidal.


6. $\mathrm{ICl}_{4}^{-}$: 4 bond pairs and 2 lone pairs, so its geometry is square planar, not square pyramidal.

So the number of species from the given list that have a square pyramidal structure is 3.