Our Priest in his homily referred to the Angels as "reflections of God" and made the comparison to the facets of a diamond; God being the diamond, and the angels his facets. Does this sound right?

No, it does not. Angels do reflect God's glory, as do all creatures to some degree. But angels are creatures, distinct from God, they are not a part (or facet) of God. 
 
Some sympathy for the preacher may be in order however. Sometimes analogies go wrong in live preaching. I suspect what Father meant to say was that angels reflect God's glory in different ways. The Seraphim are the "burning ones" before the Throne of God manifesting God's fiery glory and love, the Cherubim manifest God's glory and will toward creation, and so forth. 
 
I rather doubt Father thinks of angels as part of God. I think his analogy slipped or morphed and that by facets he does not mean to imply the angels are of the same substance as God, but rather, that they reflect his glory differently as facets or a gemstone reflect different qualities.