I would say "please...."
but I don't read offense into "Kindly..." - even without knowing it was from a non-native english speaker - I would first consider it to be a regional thing. Knowing it was from a non-native english speaker would really cause me to not think twice about it.
If it is a situation where you are trying to explain to the colleague a difference in how the two could be received -the explanation of order v request might put it into an understandable context for them.

In conclusion - I don't have strong feelings about it either way. For me, it is a tie.