DIAGNOSIS White flakes are spent ion-exchange resin beads. Black specks are granular activated carbon fines. Media is escaping from a damaged filter.
FIX Immediately discard the water and the filter. The filter cartridge is defective or was damaged during installation. Install a new filter and prime it with two full cycles as normal.
IF THAT DIDN'T WORK Inspect the filter housing inside the reservoir. If the internal grate or seal is damaged, it can fail to contain media from any filter. The reservoir may need replacement.
HEADS UP Do not consume water with visible media in it. While the materials are food-grade, the filter is no longer functioning correctly.