Studying at flame is an expression which is usually used to describe a state of deep contemplation or intense learning. Some common synonyms that can be used to replace "study at flame" include words like delving, examining, scrutinizing, pondering, contemplating, and analyzing. When doing research, one may say they are "sifting through" information or "digging into" a topic. For those in a reflective mood, they may say they are "meditating on" something or "introspecting". One could also say they are "immersing themselves" in a subject or "absorbing the knowledge" they are learning. These synonyms can be useful when trying to diversify one's vocabulary and express oneself more eloquently.