Is it safe to eat new red potatoes fresh out of garden that has pink streaks in them? What are these pink streaks?
According to the picture on this site and the description, it seems as if certain potatoes have a natural streaked coloring inside: http://antiquityoaks.blogspot.com/2010_05_01_archive.html (scroll down a lot or press Ctrl+F or Cmd+F and search for "potato" and it should move the focus to the relevant part of the page.
In addition to this particular variety, you may also come across some cross-breeds or deviations from the norm. Plants, like all living things, have recessive genes, and occasionally you may find some showing themselves in one plant but not another (so you could get a bunch of potatoes and find some that have slightly different coloring than other). This is actually not a bad thing. Having crops that are genetically diverse increases the likelihood that more will survive if there are pests, fungi, infections, etc. This is because differences in traits can give certain plants an advantage over others -- a slightly different coloring could make the root less tasty to pests, or a difference in pollen or flower color could attract more pollinating insects, etc. It's actually less natural (and less adaptive, biologically-speaking) to have every single piece of produce you get look the same. The reason that many pieces of produce do look similar is more because people breed them to look more uniform. But, that's more for the sake of people's eyes than it is for the sake of the plant's strength, nutritive qualities, chances for survival, etc.