I assume this fuel system is a two hose setup. Take both hoses off their nipples. Blow into the hose that came off the muffler, If the fuel lines going to and from the tank are not clogged, you should get a steady stream of fuel from the other hose with little effort. If that is so, then you have a clog somewhere after the carburetor intake nipple, probably near the needle valve. The easiest way to clean that area out is to remove the carb from the engine, take the needle valve out of it, and dump the entire carb and intake manifold into a crockpot of antifreeze and let it cook at about 225 to 250 degrees for several hours. Use the old style green ethylene glycol for this. Then rinse the assembly with water and blow out with compressed air until dry. If there is the slightest hint of a clog in that area, this will clean it out.
Actually, when I am trying to resurrect an old, gummed up engine, I don't even mess with it. I simply disassemble it as much as I can, dump it in the antifreeze for several hours, rinse it off and blow it out, then reassemble it before I even attempt to chase a problem In about 95% of the time, the engine will then start and run fine without further ado. You now have a clean engine, inside and out, that will run as well as it ever will without replacing parts. You have eliminated chasing a hard to find problem and the engine looks good.
I just recently did a Saito .91 that had been sitting inverted with fuel in it for about five years. That thing was a mess. The intake valve was stuck fully open and there was gel inside it everywhere. I completely disassembled this one including removal of the cam from the cam box because the intake lifter was also stuck in its bore. I let that one cook for about 24 hours, rinsed it off and blew it out with air and reassembled it. I use Marvel Mystery Oil to lubricate parts as I am reassembling them. I hit that puppy with a starter and it was running in just a couple revolutions.
I find it easier to assume these things won't run if they have been sitting with fuel in them for any extended period of time and do the antifreeze thing in a crockpot to them before I even attempt to start them. I would prefer to begin with a like new engine than try to chase an unknown problem in a cruddy engine. Maybe a new glo plug will do it. OK, that didn't do it, maybe adjusting the valves will do it. Nope. Maybe spraying the inside of the needle valve with carb cleaner will do it. All right, that didn't work either. I know. I'll replace the fuel lines at the tank. Nope. Not that either. Maybe, maybe, maybe..........
Or I can disassemble it, dump it in the crockpot, and build whatever wing I happen to be working on while the engine cleans itself.