Let me back up my assertions with some references. My all-time favorite aero book is NavWeps 00-80T-80, and if you look in the index, you will find climb angle. In mine, it starts on page 152, and goes on to state that max climb angle is obtained when T-D is greatest. I have a nice little book called Jet Airplane Performance, by Lufthansa Consulting, and on page 32, after giving the standard equation, it states "The smallest value for C(drag), and therefore the drag, are obtained with retracted flaps . . .. Thus, the climb gradient is greatest with flaps retracted." I have a neat book by Boeing designed only for folks who absolutely love the Calculus, (it took us six weeks to go through it!) and it gives the same equation on page 3.130. I can't find a succinct statement, but I did stick all the equations into a computer about fifteen years ago, and showed that, at max weight for a noise abatement takeoff, the 737-300 would arrive at 1000'agl about 150 feet sooner with flaps five than with flaps 15, even though with the greater flap setting, the ground roll was significantly less. Hence my hangup when folks say that flaps make you climb better.
By the by, that noise abatement climb gave me every bit as much of a rush as a good slow-roll. I loved it. But it was stupid - deck angles of 30 degrees were not uncommon! An engine seizure at that attitude in the sim challenged the very best!