A family member I'm in the process of filling a small claims suite against caused thousads of dollars worth of damage to my home. Could this person use bankruptcy to get out of paying a settlement if it's ruled in my favor?
Yes. If they file bankruptcy you are likely barred from collecting that debt.
Unless Iowa is very different than most states, you cannot bring an action seeking "thousands of dollars" in a small claims court. Your important question about the bankruptcy cutting you off should be asked to and answered by a bankruptcy lawyer in your area.