We don't have synonyms for burkha yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are burka, gurkha and bourkha.
(n) :
Alternative spelling of burqa. [(strictly) An enveloping Central Asian garment which covers the whole body, incorporating a netted screen to cover the eyes, chiefly worn by women in fundamentalist denominations of Islam to observe sartorial hijab (the practice of wearing concealing clothing in front of adult men after the age of puberty).]
(n) :
Alternative spelling of burqa. [(strictly) An enveloping Central Asian garment which covers the whole body, incorporating a netted screen to cover the eyes, chiefly worn by women in fundamentalist denominations of Islam to observe sartorial hijab (the practice of wearing concealing clothing in front of adult men after the age of puberty).]