how to pronounce "Daniel Dunglas Home" correctly in american english?
It is important to remember that this is a Scottish name and as such has a different pronunciation to English as spoken in England.
"Daniel" would be pronounced as you would expect.
"Dunglas" would be said as "dung-glass" with full emphasis on the double-s as you would pronounce the word "glass" - not the short, clipped "lus" as some English names/words might be said.
"Home" is pronounced as "hume" (also the same as the place name / surname "Hulme"), as the Wikipedia entry you quoted from suggests.
Whenever faced with pronouncing any non-English name, it is a choice to attempt an accurate pronunciation in the original language or accent, to Anglicise it, or to make a compromise between the two. If you follow my guide above, I believe that should be a satisfactory English pronunciation of the Scottish name.
This documentary about the man is a good source to hear his name pronounced.