Learning how to choose integrated DC to DC boost converter
300 mA out at 15 volts is a power of 4.5 watts and, with the inefficiency of the converter you will need to supply about 5 watts from the 3 volt battery (or 1.67 amps). However, the output resistance of a Duracell CR17345 is about 0.25 ohms and taking this amount of current instantly drops the battery terminal voltage from 3 volts to about 2.6 volts. You are now on the slippery slope of it never working - the voltage drops and your DC-DC converter demands even more current to get 5 watts it needs to sustain 15 volts on the output at 300 mA. 



See how the battery terminal voltage has dropped to about 2.6 volts with a load current of just 1 amp after only 6 minutes - given the output resistance is 0.25 ohms, a 1 amp load will immediately cause a voltage drop to 2.75 volts.

The LT3495 requires an input voltage of at least 2.5 volts so after a few tens or maybe hundreds of milli seconds it will shut down then burst back to life (as the load is removed due to the shut-down) then continue repeating this and flashing the display on and off cyclically.

You need to find a display technology that isn't so hungry or, have a better battery.