| Cantriped |
A Flaming Rune is 9th level, so no go there...
There should be a low-level alchemical or magical item which grants one or more strikes worth of extra elemental damage... but I cannot find one. Seems like something that could/should be added to the final Rulebook. But that doesn't help your player much I'm afraid.
Personally I think low-level alchemical items that you applied to a weapon (like silversheen) to cause it to deal extra elemental damage, or give off light, or whatever would be really appropriate and useful for all sorts of alchemists.