glennacno, NI-MH cells like eneloops will work
a 10440 is a li-ion cell, so it runs at a nominal voltage of 3.7v, as opposed to an alkaline with 1.5v, and NI-MH at 1.2v
legopikalegopika is correct.
All flashlights should have a voltage range listed.
If you want a flashlight in single AA or single AAA form factor that could take either alkaline or rechargeable Lithium batteries, the voltage range should be 0.9V-4.2V (or wider). The high end of the range to cover a fully charged Li ion, and the lower end so that as an alkaline drains and the voltage drops, it will still keep working.