Why would the brain flip the images perceived by your eyes?
It is not meaningful to talk about your brain processing something as 'right-side up&quot;' or 'upside-down'. The 'images' in your brain are just collections of neural activations, and not actual pictures. Thus they cannot have an orientation. The only meaningful way to test your question is to try flipping the input the brain receives and seeing if it can cope.
Fortunately, the brain is capable of flipping your visual field if required as measured through perceptual adaptation experiments using inversion glasses. This has been demonstrated very drastically in studies, by for instance requiring a participant to wear inversion glasses for a long time. At first they are confused, and unable to orient themselves and do basic tasks, however after enough time the brain can adopt enough to even do activities like riding a bike. This suggests that from the only way you can measure things (i.e. behaviorally) the brain is capable of adapting to an upside down world (some participants even reported that after extended use the world even seemed &quot;right side up&quot;). This is functionally equivalent to the brain being able to process your visual information in either orientation. If it is capable of processing in either orientation, the question of &quot;does my brain flip the image&quot; becomes a pseudo-question and unanswerable.
References

Taylor, J. G. (1962). The behavioral basis of perception. New Haven: Yale University Pres

Harris, C.S. (1965) &quot;Perceptual adaptation to inverted, reversed, and displaced vision.&quot; Psychological Review 72(6): 419-444. [pdf]]

Di Paolo, E.A. (2003) &quot;Organismically-inspired robotics: homeostatic adaptation and teleology beyond the closed sensorimotor loop&quot;, {Dynamical systems approach to embodiment and sociality: 19-42 [pdf