I will be traveling by coach (Flixbus) from London to Paris. I'm an Indonesian citizen with both tourist visas for the UK and Schengen area. From my understanding, there are usually two border control checks (one for leaving the UK and one before entering the Eurotunnel). France will be my first point of entry in the Schengen area so will the French authority stamp my passport when we get to the border control? and will the British authority also stamp my passport for exiting the UK?
Border control for both countries happen together before the tunnel no matter which direction you're traveling in. (Source). These happens by a special agreement between the UK and France ("juxtaposed controls").
The UK does not use exit stamps for anyone -- but you can expect the French guards on the British side to stamp your passport with for a Schengen entry.
Anecdotal reports suggest that the French sometimes don't give an entry stamp. If that happens, try to politely insist on getting one; it may create trouble for you when you leave the Schengen area if you can't document when you entered.