Yes, they stack.

Bestial Aspect says:

If the rageshaper's bloodrage powers already grant natural attacks or alternate modes of movement, then the bonuses granted by bestial aspect also apply to these bloodrage powers.

So, its bonuses apply to the claws granted by Draconic Bloodline.

The damage progression of the claws is similar to the damage progression of a monk's Unarmed Strike - their fists don't get any bigger, they just get better at using them.

The only mention of size in the description of the claws, is to say that Small characters have a smaller damage die. (Again, similar to Unarmed Strike)

So, neither effect makes the claws bigger, just better.

Yes, they stack.

Bestial Aspect says:

If the rageshaper's bloodrage powers already grant natural attacks or alternate modes of movement, then the bonuses granted by bestial aspect also apply to these bloodrage powers.

So, its bonuses apply to the claws granted by Draconic Bloodline.

While the damage progression of the claws is similar to an effective size increase, it is also similar to the damage progression of a monk's Unarmed Strike.
(Which could maybe be argued as an effective size increase too, but that's irrelevant because...)

Bestial Aspect however, doesn't bear any resemblance to a size increase. Your die doesn't "increase by one step", it increases by one die. Meaning, your 1d6 claws become 2d6; your 1d8 claws become 2d8. So there is no stacking of effective size increases.