While no seasoned pro at PI yet but deep enough into it to know something about what one can do in tweaking emitters, I feel it would be very possible to do so.
The clip you showed is too far-field to get a sense of the birds, and I don't know how detailed and/or near-field you want your flocking to be, but here is what I would do:
--- Choose an emitter that approximates a moving-veil or flame type movement, that is a general feel of flocking.
--- Depending on the emitter type (point, area, etc.) replace the particle type or types with a custom made "particle type", i.e. a bird or various shots of birds.
--- You may wish to check out Paul Hansen's third particle library* with the birds in it and maybe use that as a starting point for creating this, creating and using smaller sized images of these individually. Or creating your own).
--- Then start crafting the effect you wish as a project file and save often. Once satisfied, you can then import it as an emitter into the libraries. I often have various versions of the same, so I can go back and use them if I over-tweak something :)
Bottom line: With some patience, ingenuity and creativity, PI is very versatile for creating a wide-range of effects.
But Gentle Warning:
--- Using images as particles that are more than 8-bit, sequences and/or large will use alot of preview rendering and CPU juice. If your system can't handle it well, you're going to have to do this slowly and carefully.
So check with PI sales or support for such requirements.
* >>> Here is the mentioned particle library by Paul Hanson -- the bird one is the third on first row: