The rules for joining boxes with box-decoration-break: slice currently say:
For boxes broken across lines
First, fragments on the same line are connected in visual order. Then, fragments on subsequent lines are ordered according to the element’s inline base direction and aligned on the element’s dominant baseline. For example, in a left-to-right containing block (direction is ltr), the first fragment is the leftmost fragment on the first line and fragments from subsequent lines are put to the right of it. In a right-to-left containing block, the first fragment is the rightmost on the first line and subsequent fragments are put to the left of it.
The normative text seems to say that it's the inline element's own direction, but the examples both refer to the containing block's direction. It should be clear which one is used.
(I got here as part of filing Mozilla bug 1632228.)