There isn't a specific amount required to start a record company. Still, you should have a business plan that is sustainable in the long run, as the music industry is constantly evolving with advancements in technology and changes in how people consume music.
A business without a strategy to generate revenue is definitely going to tank hard. Almost anyone can start a record label. It's not rocket science, just like setting up a new company. The challenging part is turning a new company into a reputable business.