Can I claim the flat damage fee written into my motel's terms?

You can put the clause in front of the judge, and it will be read as evidence rather than as an instruction. Small claims exists to compensate proven loss, and a court examines whether a fixed sum in a contract is a genuine attempt to estimate damage that would be hard to quantify, or a penalty designed to punish. A flat figure applied to any damage, from a broken lamp to a flooded bathroom, tends to read as the latter, because it obviously does not track the actual cost of anything. What usually happens is that the clause is set aside and you are awarded what you can document.

There is a version of this that works better, and it is worth changing your terms to get it. Instead of one blanket minimum, publish a schedule that reflects real replacement costs by item, with the age-adjusted figure you would actually charge. That is defensible, because each line is a genuine pre-estimate rather than a deterrent, and it also means the guest was told the specific consequence in advance. Keep the clause as support for your documented number rather than as a substitute for documenting it, and you get the benefit without inviting the argument.