Looking at the link to rivet tools that you sent, it appears to me
that implies you are working with hollow rivets - which I did not
understand from your original query. I had assumed, on the basis of
no that you were asking about how to upset and seat
solid rivets - which is what I think of when I see the word rivet.
Apologies if my helpful hint isn’t helpful with hollow rivets which
require to be flared from the inside out.
However, I imagine that a tool similar to the one I described
originally could be made to operate on the same principal, that is,
burnishing the rivet into shape with a rotating tool rather than
hammering or pressing it into shape. The tool would have to be
shaped to suit the rivets you are using, not a hard job really - a
pointed, tapered end which would enter the rivet stem to start the
flare-out with a wider section like a shoulder to work the flare
further out and down against the metal surface. The largest diameter
of your setting tool should not exceed the final diameter of the
rivet head. The tool should be used in an electric drill, pressed
down into the rivet stem while running the drill with a slight
wobble (or precession, as astronomers like to say) to get the outer
edges of the rivet head out and down tight against the surface.
The other end of the rivet would have to be supported, of course,
against bench top or other solid support to keep the head from being
pushed back out of its hole.
Good luck. Let me know what you decide.
Marty in Victoria BC, A good head, really.