In original versions, on PS1, when you pressed SELECT+R1, Lara was using Flare from her backpack.
You can do that in Remaster as well. Provided you play on a controller.

Better yet! With other button combinations, you'll make Lara do other things (PS1 had only Flare shortcut).
Using TR3 as example:

BACK+RB / SELECT+R1 = Draw Flare, Throw held Flare

BACK+A / SELECT+X = Draw Pistols
BACK+B / SELECT+Circle = Draw Shotgun
BACK+X / SELECT+Square = Draw Desert Eagle
BACK+Y / SELECT+Triangle = Draw Uzis
BACK+LB / SELECT+L1 = Draw MP5
BACK+LT / SELECT+L2 = Draw Grenade Launcher
BACK+RT / SELECT+R2 = Draw Harpoon Gun

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Edit: Added descriptions for all shortcuts that I've found

I totally forgot about these shortcuts.
The flare shortcut is particularly useful as you can't bind that to gamepad currently, even though there's a dedicated keyboard binding.