Flashing LED's incorporate integrated electronic circuits that takes care of driving the chip. Efficiency/brightness is not one of their design criteria.
Be aware that ultra bright is not neccessarily the same as efficient. A high mCd rating can be achieved by simply narrowing the beam.
You probably want wide-angle LEDs with a relatively high Lumen per Watt rating, but also with a relatively warm & nice tint like 3-4000K (not a bluish 5-7000K).
If the Lm rating is missing you can calculate it (approximately) from the mCd & angle spec's, with the help of calculators you find on the 'net.
Cree makes a lot of different LED's, with different current & voltage ratings. You have to be more specific. Conditions = specifications.
A single white or blue LED chip has a voltage drop of about 3-3.5V so you can put two (or even three) in series with a resistor, running them off 12V.
If you apply a resistor + pot setup to high power LED's though it'll waste a lot of power, which you don't want with a solar setup. Use a dimmable switchmode LED driver.
They're made for many different input & output voltages, & output currents.