In a standard segmented ring where the segments are cut from a long board, the grain runs around the bowl making it an edge grain (I call it side grain) ring. If you make a ring of chevron or diamonds where the blade is tilted by 45 degrees, for example, the ring is neither flat or edge grain but this does not mean that the ring is likely to delaminate.
The thing to consider with regards to grain is that the strength of rings in a bowl is not determined by the glue between the segments of a row. The holding power of glued rings comes from the glue between the rings because there you have flat grain glued to flat grain. If the ring is made from chevron or diamonds, there is still enough side grain glued to side grain to maintain the integrity of the bowl. Where problems arise is where you have end grain glued to side grain. When this is the case, there is no integrity between segments and no integrity between the rings and a bowl like that is likely to delaminate over time.