Does Brynhir stop the rest of the cards on the Promisng Future chain?

No, Brynhir Thundersong does not stop the rest of the cards on the Promising Future chain from resolving.

According to RiftJudge FAQ #229:

When Brynhir Thundersong is played from Promising Future, any other cards already played via Promising Future that are currently pending on the chain will still resolve normally.

Why this happens:

1. Pending vs. Resolving: Brynhir's "When you play me" (WYPM) ability prevents players from playing cards (taking them from a zone and placing them on the chain).
2. Existing Chain Items: Cards already played by Promising Future are already pending items on the chain. They are not being "played" when Brynhir's effect takes hold; they are already in the process of resolving.
3. Resolution Order: When Promising Future resolves, it places all chosen cards onto the chain as pending items in turn order. Once the spell finishes, these items finalize and resolve. Brynhir's triggered ability resolves, and her effect goes into place, but this only restricts new cards from being played from zones like the hand. It does not retroactively cancel or stop items that have already been placed on the chain as pending.

Sequence:

• Promising Future resolves, and players place their chosen cards onto the chain as pending items.
• Brynhir (if chosen) finalizes and resolves, putting her "cannot play cards" effect on the chain.
• Any other cards already placed on the chain by Promising Future proceed to finalize and resolve normally, as they were already in the "pending" state on the chain before Brynhir's effect became active.