I've looked it up and there doesn't seem to be an answer that works for me. Im playing Fallout 1 and there doesnt seem to be an option in the inventory to light the flare. Anyone help?

Right click in the flare and select use option. After drop off the lighted flare for you inventory to light the area.

Go into your inventory screen and bring up your flares in the left-hand vertical scrolling menu. Right-click anywhere on the screen and your point should turn into an arrowhead instead of a pointing finger. With the arrowhead, click on the flare and a menu of pictures options will appear. Carefully move your mouse down until the "Use" hand is highlighted and then click it. This should light the flare and it will drop to the bottom of your inventory screen, so you have to scroll down to see it. From here, you can either put the flare in one of you inventory slots to light up your area as well as throw the flare for 1 AP, or if you put the lit flare back into your inventory list (with the pointer finger) and then select it with the arrowhead, there will be an option to drop it on the space you're standing on.

This is the best video I've found demonstrating how it's done: https://youtu.be/lKzaecCilpw?si=EFaJaxDejplN0Gbb&t=40

10 years later and there was still no answer written anywhere that i could find, so here it is. Happy trails vault dweller!

You need to change your cursor for the arrowhead and then click and HOLD the left button on the flare, after that, you move your mouse up and down to choose what to do. Today, after deep investigation I found out you can use items from inventory and don't need to equip them in your hand :-)