[ Shakuyaku • 芍薬 ]
'Chinese peony' ; also called the "flower minister" to the tree peony's "flower king"
[ Kagan • 火岩 ] 'fire' 'rock/crag' ; 岩 is not a kanji I have seen before but given the context and its usage throughout the series, it might be an anarchiac way of writing it? :\
[ Shakugan ⚛ 灼岩 ] 'miraculous' 'rock/crag' ; note that 灼 is a combination of 火 and 芍 (without the top radical)
[ paeoniaoxylon ]
"Paeonia" - from the genus Paeonia, which consists of peonys.
"-oxylon" - supposedly used as a suffix for extinct petrified wood fossils(?), such as with
Palmoxylon (petrified palmwood) and
Araucarioxylon arizonicum.
Petrifed wood - literally "wood turned into stone" ... It is the result of a tree having turned completely into stone by the process of permineralization. All the organic materials have been replaced with minerals ... while retaining the original structure of the wood.