Will a V-Y surgery on both lips run a risk of the scars inflaming during oral sex?

Well healed incision scars should be fine 3 months after surgery. I don't think they are likely to get inflamed. Remember, your lips are moving all the time with speaking, eating, and drinking so motion around the incisions is expected. I assume the scars will be inside your mouth so they will not be visible.
However, there may be other options for enhancing your lips. A photo of the area may lead to other options that could work well.