C’est du mon riz is impossible because it would be using two consecutive definite determiners:
– le, article and definite determiner contained in the partitive article du (→ de+le) and
– vos which is a possessive definite determiner.

But one could have:

C’est de mon riz.

and

Ce sont de vos chaises.

where de is followed by just one determiner.

Having de in front of the determiner indicates that you designate a certain amount, not all your chairs, my rice, etc.