I did a quick test with SIL's free Padauk font
and got the same results, which indicates that there's a problem with the Qt rendering engine. (Both Calibre and Sigil use the Qt rendering engine.)
Since Burmese is a relatively rare language, you may want to log a but report with the Qt developers
. If they fix this issue, future Calibre and Sigil versions might eventually be able to display Burmese correctly.
Since it's very unlikely that any of the current Adobe Reader Mobile SDK based ePub2 readers will be able to display Burmese correctly, you'll have to create a PDF version of your book for these devices following the instructions in this PDF created by Sony
BTW, the book seemed to display fine in Readium and Kindle Fire Previewer. I.e., you might be able to read your book on an iPad, a Kindle Fire or other Webkit based eBook readers.