What does the chain of Hawaiian volcanoes record as it gets older toward the northwest?

Answer: The Pacific Plate moving over a hotspot

The Pacific Plate moving over a hotspot ✓ — Correct. The Hawaiian hotspot is relatively stationary, and the Pacific Plate moves over it. As the plate drifts northwest, volcanoes are carried away from the hotspot, and new ones form above it. This creates a chain of islands with ages increasing to the northwest, recording the plate's motion.

A westward flow of lava over time — Lava does not flow thousands of kilometers to form a timed island chain. Individual eruptions are local, and the age progression across the islands is due to the plate moving over the hotspot, not lava traveling. The youngest volcanoes are near the active hotspot, while older ones trail away.

Erosion selectively exposing older rocks — Erosion does shape the islands, but it doesn't create the age progression. Older islands are more eroded because they've been away from the magma source longer, but the fundamental record is the plate's movement over the hotspot. Erosion is a secondary effect, not the cause of the age pattern.