We have orange trees that have always produced "orange flesh" oranges. This year a few of the oranges have red streaks in them. Is is possible that this year the flowers were crossed with a blood orange tree?
This has nothing to do with what pollinated your trees this year.
But apparently some of your trees have a trace of blood oranges in their ancestral line. Oranges (Citrus x sinensis) are a hybrid between pomelo and mandarin and all citrus are rather prone to hybridization and mutations.
So why do you suddenly see red streaks?
I blame the weather. Did you have cool nights and warm days lately?
To develop the deeper colours, oranges need a certain temperature gradient which causes "blond" oranges to turn from greenish to orange and blood oranges to develop their crimson colours. In very warm weather, oranges ripen, but stay paler. (See my answer on Seasoned Advice for more details.)
Update: This answer is wrong and doesn't help anybody. Although at first I have deleted it, I now have decided to undelete it so that I just have a reminder on the long journey that awaits me on this site. For every upvote (+10 points) I will need 5 downvotes (-2 points each) in order not to unethically increase my rep on a wrong answer, so please be careful and do NOT upvote it. Thanks!
Old answer: Yes, it is possible. Blood oranges are a variety of the orange ones, Citrus × sinensis. Plants in the Citrus genus (like oranges, pomelo, tangerins, mandarins and others) are well known for their ability to produce hybrids. For the crossing to occur, some blood orange trees need to be nearby.