If I got an Amex card, but didn’t make the required spending amount, then cancelled it and reapllyed, would I I eligible for the bonus?
Only AMEX can answer this, but cancelling the card and attempting to reapply would probably not get the response you seek.
You would have to check the details of the exact bonus offer you are trying to get, as AMEX has varying promotions all the time. My general experience is that there are time restrictions like “New cardholders only. Not eligible if you have held any AMEX product within the past 12 months”. Some are looser and say you can’t get the bonus with X amount of time of receiving a previous bonus.
So, it depends on the original offer you got and the terms of any new offer you are considering.