Dust is a mixture of different things, that is the reason that can posses charge.

Dust particles do not have charge in it, it is the charge of the substance that is attached to it that can flow the charge to the dust.

Explanation:

When the dust particle is attached to a charged substance it possess charge. The charge of the substance make the dust particles polarize to make it charged.

For example, when the dust particles sticks to a tv screen then it is not the dust charge that make it stick to the screen, it is the charge of the tv screen that make the particles attached to it.