Can you just take the tires & wheels and not the car?
Or air up the spare?  I carry two cans of non-explosive tire inflator
stuff for emergencies.
Besides destroying the wheels, pieces of tire will fly off and hurt people.

Not a good idea for many reasons. Rim damage, Brake line damage, tie rod
or strut damage from a tire that pulls off the rim.
Two flats from what damage? The rims may already be bad unless it was
because someone cut the tires when it was parked. Even at low speed it
will probably damage the rims because the tire will tend to slip to one
side or the other instead of staying under the bead areas.

I would get a buddy to run me down to the shop with one set of rims.
Then bring them home and install them and then drive down and get the
other two replaced. Take one of the tires that is still up to use as a
spare unless they are mismatched (like you have 4 aluminum rims and the
spare is steel.

I wouldn't drive more than a block or two on a flat.  It's just asking
for trouble, as others have already pointed out.

At this point I'd invest in some jackstands, put the car up in the air,
and run the wheels and tires to the shop in another vehicle.  It's
really the only way to do it.  If you can't borrow a car renting a
pickup or van is probably cheaper than the tow bill.  Don't forget to
take the car back in for an alignment check after you're done.

Since your spare is flat, I'd recommend if it is a full sized spare
whose wheel matches your other ones, to take that in and have a new
tire mounted on it, and keep the better of your non-flat tires as a
spare, as it's likely newer than your current spare and also is known
to hold air.

Even if you have a "donut" spare, if you live in an area where flats
are common (I used to live in Dearborn, MI - never had so many flats in
my life anywhere else, the roads there are awful) it may be worth it to
get a matching full sized wheel from a junkyard and have one of your
new tires mounted on that, and then you can keep an old wheel/tire in
your garage/closet/whatever for situations just like this.  I did this
for my GF's Sentra when we lived in Dearborn and IIRC it cost me about
$25 or so, although the junkyard was a good 20 miles away.  Fortunately
all of our other cars were Volkswagens which used the same bolt pattern
so one tire covered all of them.  In fact, ISTR using the spare from my
VW on her Sentra for a couple blocks when she hit a pothole while she'd
already had a flat, although that's not a particularly good practice
(lug seat style mismatch)

good luck,

nate

Don't do it.  Take the flats off, put the car up on blocks, and get
a friend to drive you with the three rims to the tire store.
--scott

Take off the flat tires and cab it, or ask a friend, back and forth from the
tire place.  Cheaper than a tow.  
---------------
Alex

Why not put the car up on jack stands and put the wheels with flat
tires in another car to take to the tire shop?

Flat tires are very easy to fix.  Go to automotive store or gas station
and get flat fixing kit, and not that can stuff.  You just find the
hole, rought it up a bit with this ribbed pole, then jab in a piece of
rubber covered with rubber cement.  Then snip off the excess.  I keep
one of these kits in my car at all times.

I wouldnt drive on flat tires.  Can you make it to gas station and fill
them?