I've checked lots of tackle for flights without incident.
I have checked a Marcum flasher without a problem.
Check the FAA/TSA rules for hazardous and prohibited items such as gasoline, propane, certain types of batteries, lighters, etc. Carry on restrictions ban tools such as forceps, pliers, knives, jaw spreaders, multi-tools, spuds, gaffs, hand augers.
They may all go in checked bags if you can figure out how to pack them to avoid damage to them or to your bag/airplane/handler.
Whatever you check, pack it well with padding all around. Be sure rods are padded and in a sturdy rod tube. Fold reel handles and wrap in bubble wrap or use clothing for padding. You can be sure your checked bag will be dropped, slammed, and on the bottom of a big stack at some time.
You can typically carry on nonmetallic rod cases if they are short enough to fit in overhead compartments.
Sometimes hooks and lures will set off TSA inspectors, so I always check them.
If in doubt, ask the airline, but don't expect to get the same answer twice. When in doubt, check it or leave it home. Some folks are now sending fishing gear ahead by UPS/USPS if they have time and a firm destination. That can be less expensive than paying checked bag fees.
These days every piece of luggage gets X-rayed. If an inspector has any doubts, they will open the bag and see what is inside. If so, they are supposed to insert a note to that effect. Yes, my bags have been opened, but nothing was missing.
Good luck and tight lines.