There are three separate issues in play here.
First, TSA does not allow flash lights longer than 7" in carry on baggage. They use the same 7" standard for tools in general.
Second the FAA is the controlling authority on batteries on aircraft. They allow lithium metal and lithium ion batteries up to 100 watt hours in size to be carried as carry on baggage. Above that, they still allow them up to 160 watt hours, but only with airline approval, and with not more than two spares.
They are actually more restrictive on lithium batteries carried as checked baggage. This is because if a lithium battery shorts and starts to burn in the cabin it can be extinguished by the crew. However a burning battery in the inaccessible baggage area is a serious threat to flight safety. As a result, lithium batteries carried as checked baggage must be no larger than 100 watt hours, must be installed in the device and no spares can be carried. In addition, devices like flashlights that heat up when activated must be protected from activation.
Third, there is the "tactical" issue. Much of this makes no sense as I can bring a knitting needle, a sturdy well built roller ball pen, or a 7" long phillips screw driver, but I might not be allowed to bring my S&W tactical pen on the plane - even though the roller ball pen, knitting needle and in particular the 7" screwdriver are just as effective if I wanted to stab you under the arm.
Apparently the difference is that it is a "tactical" pen and some individual TSA screeners won't allow tactical items. What is even more disturbing is that tactical pens are not listed anywhere on the prohibited items web page - other than in a 2014 "week in review" page listing a tactical pen as a prohibited item "discovered" in carry on baggage.
Similarly you will not find any reference to or definition of "tactical flashlight", but you may find that the TSA officer screening you won't let it pass.
The problem is that the officer at the check point makes the final decision as to what goes and what does not. For example the TSA allows body armor as both checked or carry on baggage, but a TSA officer can deny passage at the check point at his discretion. Same with hand cuffs. Same with toy water pistols.
Another classification that can cause problems are what the TSA screening officer may define as a blunt object. For example, my wife and I cave dive, and fly to Mexico on occasion to dive in cave in the Tulum area of Mexico. Cave diving requires really good lights and you usually exceed the 100 watt hour limit, so they can't legally go in checked baggage.
But...the catch is that cave diving lights are also usually cannister lights where the battery is in a can, with a cable going to the light head. I've had TSA officers object to them because the heavy battery canister could be swung by the cable and be used as a weapon. This creates a problem when you can't put it in checked baggage.
I switched to a light that had a EO cord that could be screwed off from the light head and battery cannister, creating 3 pieces. This light flies right through, even though I can just re-attach the cable to the canister and swing it like a mace once I am on the plane.
It makes no sense what so ever, and sadly it doesn't have to because the TSA screening officer can do pretty much what he or she thinks is in the interest of "safety".
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For extra fun, try flying with a parachute sometime. If you check it, and the TSA decides it needs to be inspected in your checked bag (and they will) you'll get paged as they require you to be present to inspect it. And you can find yourself repacking it when they are done. That, in addition to not wanting to trust life support equipment to baggage handlers, makes carrying it on the plane as carry on baggage a much more attractive option, one that is allowed by the TSA. Unfortunately, it will freak the TSA officer out pretty much every time and you'll end up having to show him it's an allowable carry on item and explaining exactly why you don't want to check it. Be sure to show up early.
