The lighting kit specifies it's 12v, so the 7.4v is probably not enough to run it. 12v stuff like this is usually meant for "automotive" 12v, which is normally about 13.6-14.4v in operation (if the car / etc batery is at 12v it's closer to dead than working).
So you'll probably need to return the 7.4v battery and replace it with a 12v (13.6-14.4v) battery.
Since hte light kit says it has a 5A fuse, it probably uses somewhere close to that amount of current when all lit up, though it may use less. To be sure you get a battery with enough capacity and capability, it's safer to assume it takes 5A to run the lights. If you have them on all the time you ride, then for one hour of riding you need a minimum of 5Ah, and the battery must be capable of at least 5A output. (note that A and Ah are totally different things).
Ones like this
should work, though it's only 3Ah so it would only operate for 3/5 of an hour if your kit actually uses 5A in operation and it's on the whole time. There are probably higher capacity but lower cost versions of the same thing that would work--you don't need one that can do hundreds of amps (250-300CCA is for starting a motorcycle, you only need maybe 5A current, though it's fine if it can supply more).
For wiring up the kit, ther'es an image on the kit page that shows where to connect the left and right turn signal switches. It doesn't say where they connect from there, so you'd have to check it's manual to be sure. Normally these would connect to the motorcycle's existing turn signals, which are powered on by the motorcycle's flasher unit whenever you switch the turn signal control on the handlebars on for left or right.
If you don't have a turn signal control switch, or an LED_capable flasher, you'll need both of those added to the bike to wire this to.
YOu can use motorcycle, scooter, or ATV handlebar controls, or DIY something from a regular switch. I have this one to use on my new trike; I haven't checked out it's wiring to see what connects where yet. If you use this one, you only need one of the two control units; they both have a center-off two position switch so you can use either one for turn signals, and you can use the big top switch on eitehr one to turn the lights on / off entirely if you like. Other switches can be left alone o rused for other things if you like. There are hundreds of other choices if you don't like that one. Actaul wiring could vary from unit to unit so if you can, get one that comes with a wiring diagram (I don't think this one did, but dont' remember).
I use this flasher
Get the job done with the right part, at the right price. Find our best fitting turn signal flashers for your vehicle and enjoy free next day delivery or same day pickup at a store near you!
www.autozone.com
The flasher wires to the 12v plus and minus on two pins, and the third goes to the center wire of the turn signal switch. The left wire from the switch goes to the left wire of the kit, and the right to the right.
The rest of the kit wiring you will have to verify with the kit manual.
Oh...while you might think it makes you more visible to use multicolroed or color changing lights, those are not lights that are on road vehicles, so drivers are not trained to "see" those as being something that might be in their way or that they should avoid. They are going to assume without any thought that those nonstandard lights are not on the road, but are from other sources, and unless they consciously choose to check the source's location, you won't be as visible as if you used standard lighting colors (white in front, red in back, amber for turn signals front and rear (you can use red signals in the rear but amber is more visible and also standard)).
Use a standard common communication method if you really want to get your message across to the most people in the most situations.
