You can do almost everything yourself If you are willing to do a LOT of studying ...
First go back to Aircondition.com and read the section on testing for leaks using Nitrogen and R-22...
After you flush you could call and just ask for that service to be done by a shop... or you could buy a small nitrogen cylinder.... if you are like me who looks for excuses to buy tools and equipment... ( I just got a five ft high one..but much smaller ones are available at welding supply places )
This is easily the best way to do that... and they tell why in a comprehensive way...
You can rent some of the big things you need only once and for short times.. like AC vacuum pump. If you have done all the other stuff carefully and correctly you will only need it one weekend... if not you will need it the next weekend also... but that is cheap and gives you a lot of power over the cost of your repair.
But it is nice that you got that estimate... so as you go along and find you can not rent some tools you can judge their cost against what having some shop do it ( and you not know how careful they were )....
Those other things you asked about .... like flushing... are well discussed in threads here on this forum... the search engine will bring them up...