At first, I considered make to be a clipping of make-up, if so, it would be pronounced [meiki].
But then it occurred to me that make might be a clipping of maquiagem, if so, it'd be [maki].
Which is correct?
The word is make-up, of course. I think you're talking about Brazilians who use the English word instead of saying 'maquilhagem/maquiagem/maquilagem'.
They adapt it to their own language/pronounce it using their own accent: 'ki'.
In other words, they pronounce 'make' the same way they would pronounce a word in BrPT.
que > qui
As a Brazilian who is somewhat atuned to modern culture, "make" used as short for "make-up" is common in the city of São Paulo, but it is spreading, especially in the fashion industry (known as the "mundinho" -- small world). It is spoken "mêiki".