How do you say shadow flame in Japanese?

'Dancing flame' is揺らぐ炎 (yuragu honoo) in Japanese.

揺らぐ (yuragu) - to sway

ç‚Ž (honoo) - flame

When placed in front of a noun or nominal phrase, a verb modifies this noun/nominal phrase. In this case, 'to sway' changes 'flame' into 'swaying flame' or 'dancing flame'.