There's no model SSD25TW Amana but SCD25TW model Amana. Here's answer to your problem that I found online.

The flakes are likely the coating from the inside of the icemaker try most likely. remove it from the machine and check for cracks or chips.
other possibilities include the rubber grommet for the shut-off, but the screen on the valve usually prevents it. when the icemaker calls for water, ...

There's no model SSD25TW Amana but SCD25TW model Amana. Here's answer to your problem that I found online.

The flakes are likely the coating from the inside of the icemaker try most likely. remove it from the machine and check for cracks or chips.
other possibilities include the rubber grommet for the shut-off, but the screen on the valve usually prevents it. when the icemaker calls for water, can you tell audibly if the valve is energized the whole time? it emits a buzzing noise. if water continues after the noise disappears, your solenoid will be going bad.
some icemakers have an adjustment screw beneath the front access cover... does yours have a screw next to a plus or minus sign? you can adjust the level on some models.

Here's the parts diagram for your model:
SCD25TW - P1190425WW
Diagram#8 Part location#261 is your ice maker assembly, the black flakes are likely the ice maker mold coating coming apart, and the overfill on the water is likely the ice maker module, so ordering the complete ice maker assembly#261 should fix it all

This is from www.applianceaid.com :
On the module style ice makers the printed circuit in the module head often wears and the contacts become too long and allow the ice maker to over fill