In a single word, no. The Fed can’t cause hyperinflation for the simple reason is that it can print more money but it can’t give that money away. It can only lend that money. If people don’t want to borrow, it is powerless. Now congress could give money away and so it could cause hyperinflation if it so desired.
But the reason why we are unlikely to have hyperinflation is that hyperinflation hurts the rich and politically connected that run our nation.
Hyperinflation would harm the banks who make loans at fixed interest rates and who then would get paid back in worthless dollars.
Hyperinflation would harm holders of corporate, federal and municipal debt. And who holds most of this debt? The wealthy.
Hyperinflation would also destroy the Fed. After all what use would they be if our currency was worthless?
Hyperinflation would reduce the debt burdens of the middle class, thus helping them at the expense of the banks and wealth that loaned them the money. Would the rich and powerful stand for this? I think not.
So the Fed can’t cause hyperinflation, but Congress could. But neither of them would want to do this and help the middle class borrower while hurting the rich.