Warning: This glitch has been reported as patched by our community. While this report may be a false-positive, if you absolutely cannot re-create the glitch, it is more than likely true that it's patched.

Tutorial

Equip Care Package (any will work)

Hold Right Trigger/R2 (do not let go the entire time until I say so)

Find something to climb up on (you'll get the A or X).

With Right Trigger/R2 still held, Climb Up.

While climbing up (Right Trigger/R2 still held) hold your flash button (Left Bumper, L1).

Now you should have both Right Trigger/R2 and Left Bumper/L1 still held at the same time.

It should have then switched to your gun.

Hit Right on your D-Pad and switch back to the care package.

Release Left Bumper/L1 only to throw the flash/stun/smoke grenade. (Right Trigger/R2 still held).

Once thrown, release Right Trigger/R2 to throw care package.

Retrieve care package and use, you should get a new care package.

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Extra - I would advise on using one man army as your secondary. After doing the glitch, open the one man army menu and select the same class you currently have or another with one man army.

Once you do that the care package will reappear again and you'll have more flash/smoke/stun grenades to perform this with.

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PC users, sorry I do not know the buttons you use to perform this with, the same method applies, just replace the buttons above with your keypads.

Note - You can still do this offline if you do not update the patch. Clear your downloaded content cache.