Matthew as Don has replied i think this dream you had is very special. I would call it a vision because of the symbols - whereas a dream (or conscious projection) runs in a sequence of events the symbology here seems to be at the forefront and the sequence or script in the background. Anyway just an observation of calling it a name.
If I may add further to what Don said;
First of all I love the word - nonburning flame - this is so spiritual in its meaning. When we contemplate the essence of fire in the spiritual world we see it is nonburning; it is actually made up of the fire spirit elementals. It is only when the fire is manifested into the physical does it burn because our senses which are attached to our physical body interpretates fire is hot and burns. Another muse - nonburning fire in a mystic thought - may also be connected to blood. The spiritualisation of blood may be called a nonburning fire.
My interpretation of the dog is; you have been shown a dog does not have an ego. Humans are one stage above animals in that humans have an ego and animals do not. Animals are part of a collective group of instincts and dwell in the astral realm (the realm closest to earth). Having an ego places us above the animal kingdom and the signifance of this is very important and special.
The people and yourself Matthew were in the middle of the nonburning fire without it burning you whereas the dog although also not being burnt (because spiritual fire does not burn) vanished leaving soot and ash (also profound)
Now if we look at this and keeping the thought spiritual fire may be connected to blood, the spiritual blood covers you, engulfs you in fact, maybe even protects you, (beautiful symbology) whereas the blood or spiritual fire is not needed on the animal or because the animal does not have an ego the nonburning fire does not apply to the animal and it disappears out of the message. Leaving soot and ash is extremely arcane - in fact this is sacred alchemy together with the nonburning fire.
The soot and ash left behind is the residue of spiritual activity, it is the removal of the dross. This comes from Paracelsus (that fine alchemist) Ash is likened to salt. Salt represents the thought-process in man and salt is the residue of the spiritual activity that takes place in the head. Salt is the dross left over when life has fled, it is the skull, it is the white powder left behind when the gold is extracted. It is the ash of thought or spiritual activity.
There is a mystical interchange between fire and salt. There are two salts - one born of the activity of fire while another is the salt that remains after the burning, itself a potential fire. Salt represents the inert state of death and we were depositing salt because a golden flame was rising in our soul.
When you awoke and thought - Moses, the Passover and Easter. Further symbology in a conscious state (you were consciously aware of the meaning. stunning.)
And with this - Moses, was given the Law from God and therefore he is Wisdom - the Passover, makes me think about the Blood of Protection - Easter - the Death of Christ (with His Blood) and the Risen Body of Christ; the Resurrection - which opened the door for us to enter.
well my interpretation - Matthew awesome dream very profound - given me lots to think about - especially the nonburning fire - I think you could have opened a door here for all of us.
My regards.