What fuses to check for 2007 flht that won't start

SOURCE: my 2007 fatboy ;system relay keeps failing one after just 2 miles

Sure sounds like a dead/weak battery. I'd recommened recharging battery or replacing then having both the battery (if you didn't replace) and the rectifier checked to make sure your getting enough cranking amps and voltage to recharge the system. Motorcycle batterys build up sulfer and loose there cranking amps if not left on a battery tender or used frequently over the winter, freezing kills them.

SOURCE: replaced battery, bike started fine.

To begin with, I'd have that battery load tested to see if it's any good. I've seen brand new batteries that were bad. It it checks OK, check all the connections that go to the battery. Be especially attentive to the smaller wires that attach to it. I've seen battery acid eat the wire out of the insulation leaving the insulation intact and the wire appeared fine. If the wire bends too easily, be suspect. If the wires have the "crimp on" connectors, make sure they're tight. Your problem sounds like a bad connection somewhere.

Good Luck
Steve

SOURCE: I put premium gas in my 07 sportster. It was hard

Your premium probably had ether or alcohol in it, which acted as a solvent for all the old gas gunk in the tank and lines, and gummed up the carb. You'll likely have to finish flushing the tank and lines, and rebuild the carb to clear the gunk.

Thank the gubmint while you're doing all this extra work.

SOURCE: 2000 1200 Sportster won't start

The classic indicator of a clogged idle jet is that the bike won't idle unless the choke is on. It may or may not rev if throttle is applied. If the bike has been sitting (sometimes as little as 3 weeks) the **** that is sold as gasoline will evaporate and leave deposits that clog the idle jet, and maybe the main jet.
If you can get the bike to rev, it indicates the main jet is not clogged, only the idle jet. Pull the idle jet out and see if the you can see light thru the orifice. If the jet is clogged DO NOT try to unclog it with anything that could alter the size of the jet. A straight piece of fine wire is ok, or just use carb cleaner to blow it out. If it ain't passin' light, it ain't passing fuel.
Ideally you would pull the carb off, remove all of the attached pieces, remove the idle air screw plug to remove the screw, soak the carb and pieces in cleaner, blow the passages out, and reassemble. You can likely get by with just cleaning the jets.
The suggestions of SeaFoam or other additives will work to keep the buildup of deposits down. They just don't do a lot of good when the fuel isn't flowing thru the jets.
Open your fuel cap and take a sniff. If what you smell reminds you of paint thinner, drain that **** out. it is no longer gasoline, all thought it will burn.
Good luck. Fuel additive (Stabil, Seafoam, Yamaha, Kawasaki, etc) and a battery tender are your friends when you bike is just sitting.

SOURCE: 2007 fatboy lost the 'flashing'

Your turn signals (but not your running lights), horn and a few other things are on the "accessories" fuse in your electrical circuit, I think. If the fuse is not blown, I would guess that you have a bad connection in the power lead for that circuit. I'm not sure of what I'm going to say here because I don't work on the newer bikes but in the older bikes, the "orange" colored wires carried the battery voltage to the individual components much like "red" wires used to do in most DC circuits. I'd look for a bad connection in a plug somewhere. I hope this helps but like I said, I don't know a lot about the newer bikes. I mostly work on the older bikes that the dealers will not work on any longer.

Good Luck
Steve