How deep of concrete base do I need for a 35 foot
There are lots of variables that really need to be evaluated by a Registered Engineer but you can use this site for a quick evaluation:

Flag Pole Calculator

Of course you'll need some details to figure the lateral force at the top of the pole, this comes from the size of the flag and the expected windspeed it will encounter.  You'll also need a figure for the soil characteristics.

Again I encourage you to consult an engineer since the last thing you want is for this thing to come crashing down and injure or kill someone.