In a deep skillet, heat olive oil to 350°. Add mushrooms; saute 4 minutes. Add oregano, thyme, pepper flakes. Saute until mushrooms are browned, 4 minutes. Cool. Wipe out skillet.
Combine cream cheese and cottage cheese. Fold in mushrooms, mixing well. Spread 3 tablespoons of mushroom mixture on bottom half of each tortilla. Roll up tightly, making sure filling isn't seeping from either end. Secure rolls with toothpicks.
In same skillet, heat oil to 375°. Fry taquitos, a few at a time, until golden brown, 2-4 minutes. Drain on paper towels. When taquitos are cool enough to handle. Discard toothpicks. Serve with chutney.