your Squeaky Disc Brakes are not unusual (apart from the way you spell them....
).
The usual suspects for cures are
- deglaze pads
- deglaze the rotor
- check pads for contamination
- replace pads (with different type)
- re-align caliper
- re-tighten disc caliper mounting
- retighten disc fastening
- clean disc properly (including the holes)
- true disc
- replace disc
- chamfer edge (leading edge) of friction material
- sparingly apply copper ease to pad backings
- relieve friction material so that it better matches the braking track on the disc
- cut slot in the friction material
That the squealing goes away for a short while when you use disc cleaner does suggest that the pads may be contaminated. The smallest amount of chain lube overspray, (or even the oil residue that is thrown up off the road in urban conditions) can be enough to cause problems of this sort. Once there is even the slightest amount of oil soaked into (typical organic) friction material, it can't easily be cleaned out. What happens is that as soon as the pads get hot, the oil leaches out to the pad surface again, even if the pad surface was cleaned somehow. The disc itself will almost certainly have been laser cut; the cut edges of the disc can hold oil residues too.
BTW one method that I have heard of folk trying is to soak organic pads in suitable solvent and then to remove the solvent by setting light to it. The heat plus the wicking action of the friction material supposedly draws the contamination out of the pads better than might be achieved otherwise. I've not tried it myself. What I do know is that sintered pads are noisier most of the time (a kind of grinding sound rather than a squeal per se) but are easier to clean should they routinely become contaminated with oil.
cheers