I think it could be your A/C in need of refrigerant, not a flushing.

If the mechanic did a good honest job, you shouldn't have lost the
refrigerant to soon, meaning there is a leak.

I cannot but remember, a friend's mechanic who had suggested replacing
the evaporator in my friend's Volvo ($1200), for the same reason, and to
justify his suggestion, the mechanic left the charging port open so the
refrigerant would leak.

Good luck!

I had a similar problem when the car was less than six months old.  The
problem was the radiator.  There was evidence all along the top of the
rad of staining where the fluid in the rad was leaking under pressure
and evaporating over time.  When the coolent level dropped to a point
in the rad the water sloshing sound would be heard just as you describe
it. There was never a liquid stain on the ground.  Look for evidence of
leaking all along the top edge of the rad.    They replaced my rad and
the problem was fixed.

DO NOT pull the evaporator !!

It is not a refrigerant problem.

It's a low coolant/antifreeze problem.

We see this all the time, have you local shop try and rid the cooling system
of it's air bubble.

I almost guarantee you the problem is with your coolant level.  Unlike all
the other responses I've read to your post... this has NOTHING whatsoever to
do with your A/C.

Check your coolant level overflow tank.  ADD SOME ANTIFREEZE even if it
deson't seem low.  I would also consider a new radiator cap as it may be
loosing pressure and taking on air when cooling, which is then circulating
through your lines and making the noise you hear.

I would even guess that you've recently used your heater for the first time
in a few months, and this has introduced air into the lines which results in
the noise you're hearing.

If these steps don't solve the problem, have your radiator flushed and
changed.

Willy