I grew 'Looking Glass' for two or three years, a long time ago. It's a great foliage plant but I don't recall it ever once blooming for me. It's a complex hybrid with many species in its background but I suspect that like many cane-type begonia species and hybrids, it requires some kind of seasonal variation (temperature and/or day length) to set buds and bloom.

BTW here's some info (link below) on 'Looking Glass' from the American Begonia Society; note that it is described as a "shy bloomer".

Here is a link that might be useful: Looking Glass