FEMA and other federally-funded programs are barred by law from providing money or assistance to people who have already been helped, unless the assistance they have received so far is not enough. For example, if your HVAC system is damaged in a flood and will cost $6000 to replace and your insurance company provides you with $6000 for the work, FEMA cannot give you any additional money for your HVAC. However, if your insurance company pays you $3000, then you may get additional assistance from FEMA.
If any organization—insurance company, FEMA, local government, nonprofit, etc.—gives you money to help you with disaster recovery, you should use the money as stated by that organization and keep receipts to prove how you spent that money. You may need to prove that you spent it appropriately, either to the organization that originally provided the funds, or to other organizations if you need more assistance afterwards.