Get LED that is steady to flash when voltage drops below set value using 3V battery
Taking a wild stab at this, without knowing your battery longevity constraints:

Tie the battery output to an AP1603 to step up to 3.3V from as low as 1.1V
Use a voltage reference well below 2.7V such as the LM4041 1.225V that has quescient current below 100uA, between ground and the non-inverting input of an op-amp; with bias resistor tied between 3.3V and the same op-amp input
Make a resistive divider where the top of the divider goes to the battery, middle goes to the inverting input, bottom goes to ground. The values should be set such that, at 2.7V battery, the middle voltage is equal to the reference voltage. 4.7M and 3.9M should work.
The op-amp should have low quescient current, and doesn't need any bandwidth. It acts as a comparator. The MCP6231 is appropriate - it only consumes 20uA.
Tie the output of the op-amp to a simple oscillator, maybe a 4541B for which there are many options in 3V, also with low quescient current
Tie the output of the oscillator to an LED.