By what age should I be able to consider myself financially independent?
The younger you are the better. If you can achieve this goal by the age of 25, hats off to you. I wish I'd aimed for this goal instead of wasting my time. I wouldn't have given away a decade of living under the cloud of an employment contract.
A more achievable time frame would be by the age of 40 but no later than 45.
Retiring at 45 gives you loads of time to pursue new goals and to start ticking off your bucket list. You should have at least 15 to 20 years of good health ahead of you which is a huge advantage when it comes to travel and adventure. If you wait till your late 60s, your travel plans could well be limited by the need to be close to health care facilities. You'll need to pack your heart pills, your cholesterol tablets, your insulin and your viagra. In your 40s, your mobile medicine chest is far lighter or non existent.