I hate chlorates with regards to accepted "incompatibilities", of which I abide to the best of my knowledge in pyrotechnic devices, but I love them because they are easier to make than perchlorates and work better (in my experience.) Decent colors can be achieved without metals and using less chlorine donor. They also ignite easier and don't go out as easily, again in my experience. This goes along with its higher sensitivity compared with the other oxidizers.
Though I have done some tests with chlorates to find conditions seeming to be specific for an accident to happen. Although these test suggest to me the sensitivity of chlorates as claimed by the general community are a little exaggerated, I still choose to take those claims seriously because any conclusion I come to on the contrary need stand tall against the vast dealings with chlorates giving them a "bad name."
On small scale, I have mixed stoichiometric amounts potassium chlorate and sulfur (according to 2KClO3 + 3S -> 2KCl + 3SO2) and added drops of ~80% sulfuric acid to it. Upon doing so, I observed much heat produced and redox reactions from the gases being released. Sulfur dioxide was definitely present by scent, but I imagine chlorine and chlorine dioxide were also being produced. I thought for sure the mixture would ignite, but it just simmered down and I neutralized the acid to end the test. Its been a while since I did this test and can't remember how much acid I added to the composition, but its possible I added enough that it actually diluted the composition which could of possibly had the effect of preventing the above reaction from ultimately taking place.
I added the same acid to a small amount of H3, and that was a very violent reaction. I would have guessed it the other way around. I didn't do a test on a mixture containing all three (oxidizer, sulfur and charcoal.)
I did try ~30% HCl on H3 as well. It mostly produced Cl2 and ClO2. Not much heat and no ignition.
All that said, I still keep the acids or acid forming compounds far.....far.... away from chemicals ready for pyrotechnic usage. Oh, and ammonia or ammonium compounds.