I've never heard of this variety but since it has flat leaves it isn't Allium schoenoprasum, true chives. Other than that how about emailing Burpee and asking for the botanical name?

Garlic chives (Allium tuberosum) & chives (Allium schoenoprasum) are two distinct alliums. Garlic chives have flat leaves more like blades of grass with white flowers in mid-to-late summer in looser clusters than the tight purple balls of regular chives that flower in early spring.

I checked Burpee's website & the picture with these "Allion chives" show leaves that look flat, and flowers that resemble the white flowers of garlic chives I described above, but are purple.

I am guessing they have created a hybrid of the two types. Since you are in zone 10b, I wonder if that is a concern; maybe they need winter cold as they receive up here in zone 5.Burpee's Allion chives

Thanks.. I was wondering because I have heard of a purple flowered variety of garlic chives and even a white flower variety of regular chives but I don't remember garlic chive bulbs that looked like bunch onions, like on the picture..