Well, those lyrics are not very accurate.
So I chaffed them and I gaily laughed...
"Chaff" here means to mock: his friends told him that he was deluded, but he just laughed at them because he thought they were wrong. The "-ed" ending is not pronounced very clearly for two reasons: first, because it usually isn't pronounced very clearly in actual speech; and second, because "laughed" has to rhyme with "love".
When a lovely flame dies...
The phrase "smoke gets in your eyes" wasn't an idiom before the song was written; now the song is so well-known it has almost become an idiom.
In the first part of the song, the singer describes how he was in love, but his friends just told him he was blind to the truth; "When your heart's on fire [a metaphor for being in love] / You must realize / Smoke gets in your eyes". The fire in the singer's heart is creating smoke which is making him blind.
In the second part of the song, his girlfriend has left him, and this is making him cry. He says the "lovely flame has died" -- and when you extinguish a candle flame, it often gives off a lot of smoke. So now the smoke is a result of the end of his love. When somebody asks him why he is crying, he will say it's because of the smoke in his eyes; they will think he's talking literally about cigarette smoke, but really he's talking metaphorically.