Should I increase the values for R7 & R8?
What are you trying to do with that amplifier ?
It's output will flip and activate or deactivate VPROGRAMMER (5 volts from a FTDI device) to the 3V3 regulator, depending on some 3V3 source, and the level of your nominal 15V divided by R7 (15K) and R8 (13K).
The current through R7 and R8 occurring at 15 volts, would be some 0.54 mA, resulting in 8 milliwatts (0.008 W).
At 15 Volts, the junction R7/R8 would be some 6.964 volts.
Below approximately 7.107 volts at your 15 volts input, the 3.3 volts will win (if it is available of course) and the amplifier output would invert.
Because this seems to switch one of it's own inputs (3v3), some oscillation would not surprise me much.
I'm assuming the regulator and its output capacitor will slow that down quite a bit, but i'm wondering how happy the regulator would be with that on the long term.
I'm wondering if any of these voltages will ever be reached without severe damage (to the battery for example).
Calculations are done assuming very accurate resistors and fixed voltages, both unlikely so allow for some deviation.