Can a length of stranded 14 gauge wire be used as the traveler along with 14-2 with ground when wiring 2 LED light fixtures in the kitchen? I both on hand and do not have 14-3 with ground.

No. To say it simply, all conductors must be in the same sheathing.

Thanks for the answer- Could I get some clarification- by in same sheating - is that meaning all wires must be in the same bundle of romex- i.e. 14-3 with ground romex and not romex and a strand wire? If not can I use 2 lenghts of 14-2 with ground romex and use just one wire out ot the second romex length as there traveler. I don't want to buy a roll 14-3 if I can do it safety with the 14-2 wire I have.

If not can I use 2 lenghts of 14-2 with ground romex and use just one wire out ot the second rome
No.

All conductors must be in same sheathing (outer covering) or conduit. Meaning same bundle. That ensures that all conductors are parallel to one another and in close proximity to one another.

The reason,
An electrical current in a conductor has a magnetic field surrounding it. With AC current that magnetic field is constantly expanding and collapsing. That expanding and collapsing magnetic field will induce a current in any conductive material within its range. That means a conductor run by its self, next to something like a water pipe can induce a current in the water pipe even though there is no direct contact.
Therefore, the neutral wire must be in the same sheathing or conduit as the hot wire. While the hot will create a magnetic field in one direction, the neutral will create an opposite magnetic field because the current is traveling in opposite directions. The two cancel each other out.

There are five ways to wire a set of 3-way switches.
The first is to feed switch one and use the traveler wires to switch two and wire from switch two to the fixture.
When wired this way the neutral runs with the hot travelers. The neutral cancels the magnetic field around the hots no matter which traveler is being used.

With all other ways of wiring a set of 3-way switches one of the two travelers legs takes the current from switch 1 to switch 2. The third common leg takes the current from switch 2 back to the box that contains switch 1. There it is connected to the hot going to the fixture. Therefore you have a magnetic field in one direction on one of the traveler legs, and an opposing magnetic field around the common traveler. Again cancelling each other out. For that to happen the conductors must be parallel and adjacent to one another. So NEC code says same cable.

With DC current you don't have to worry about this. DC current has the magnetic field surrounding the conductor but it is constant. It is the expanding and collapsing of the magnetic field that induces the current in another conductor.

You should be able to buy 3-wire Romex by the foot at Home Depot or Lowe's. If not come by my house and I will give you some.