Is it possible to use a chain for a double crank on a triple crank?

yes

I bought a new cassette ULTEGRA 6700 11/25 and a new chain Ultegra 6701 on the back of the chain box it says only for use with double crankset. I have a triple, what kind of issues will I be looking at if I try to use it?

My only guess is that it is a shorter chain. It may not have come with enough links to be long enough for a triple drivetrain. Count the number of links on your old chain and compare with the new chain. If you have enough, you're good to go.

That makes no sense since a triple chain distance is actually shorter when it's on the "granny" gear. The only thing that makes a chain path longer than using it on a road crankset is if the derrailleur has a longer cage to deal with a third crankset ring.

Give it a try. If it's long enough to deal with the big to big combo then it's long enough. If it's too short then box it back up and return it for a chain with more links to use on your touring triple crankset.

You can use that chain with any crankset. As already noted, it has nothing to do with chain length. Triples do not need a longer chain. You can use the same big/big plus 1 inch method regardless of the crank. That method suggests the shortest possible chain.

The chain I'm running now according to the bike manufacturers website specs sheet has 112 rings while the one I've got has 114 so from what you all have said I should be able to use it.