Assessing fire hazard of compounds
I guess I don't completely agree with the premise of your question. Gasoline is highly flammable, even potentially explosive, yet "amateurs" deal with it constantly. The key is that it is stored and used properly, from the pump to your gas tank. It becomes less safe if you pump it into a gas can, but gas cans also have certain requirements for storage safety.

So I think the issue may be what sorts of flammables would an amateur have a high chance of storing or using inappropriately. For example, any pyrophoric compound would be a good candidate to avoid, as most require a way to exclude air and moisture, which often requires specialist equipment.

Solvents with low flash points and high vapor pressure should also be treated with respect, but rubbing alcohol (isopropanol) or acetone might qualify for that designation. Storage in airtight fireproof containers in cool and dry places is often sufficient. Better yet, use a flammables cabinet. This simple step is something an amateur might skip for cost, but it may be the most sensible precaution. I have flammables cabinets, and I use them for ordinary hardware solvents along with experimental chemicals.

Finally, work safely! No flames, as they say in organic chemistry. Use hotplates or heating mantles rather than burners. If you must use flames for some reason, put away all flammables and keep them a safe distance. Pay careful attention to any spills and attend to them immediately before resuming work. And perhaps key for amateurs, small quantities! No need for an amateur to have gallons of flammables on hand. Even professional labs are trying to reduce quantities in the name of green chemistry.

EDIT: My go-to source for using and disposing of hazardous chemicals is Hazardous Laboratory Chemicals Disposal Guide by Margaret-Ann Armour. In addition to disposal techniques, each chemical has an extensive incompatibility section about what combinations can make a chemical even more hazardous, and all these entries have literature references. I use this book literally every time I do an experiment. It deals with much more than flammables, but flammables are definitely present.