Hey! Here's the explanation on boost chaining and everything you need to know about how to boost chain, when to use boost chains, and finally, advanced techs that you can only perform by boost chaining.
First, how do you boost chain? To boost chain, do a drift, boost while you are drifting, then release your drift. Think of doing a boost while stutter drifting (stutter drifting is tapping drift to do a micro realignment). When you use a boost chain, your speed is multiplied by 1.196 times what it was when you did the boost (to keep the math easy, I will explain the calculations as if the multiplier were 1.2). A good way to practice this is by picking power gear on Babylon Guardian.
Second, how do you apply boost chaining to get the most out of it? You boost chain whenever your multiplied speed would be higher than the speed a normal boost would set you to. Situations, where this occurs, includes getting an X rank trick (at levels 1 and 2), boost chaining from your drift dash, boost chaining from your previous boost, and boost chaining from certain type shortcuts such as the second rail in Metal City or the fly hoops in the monkey ball section in Sega Carnival.
Finally, what are the advanced techs you can do which abuse the mechanics of boost chaining? There are currently 3 techs that every normal boosting gear can perform. Jump Cancel Boost Chain (JCBC for short) is performed by charging a jump, then inputting a boost chain. The jump charge cancels your boost duration, meaning that you can perform this tech multiple times in quick succession. Boost cost air though, meaning that if you mash JCBC too much in an area where you don't get any air refill (or in an area where you can't release your jump without jumping, such as going into a QTE or finishing a race), you will get punished. There are two more techniques you can perform using JCBCs, JCBCDPC, and JCBCBC (short for Jump Cancel Boost Chain Dash Panel Cancel and Jump Cancel Boost Chain Bonk Cancel better known as "Bonk Dash"). Both of these techniques perform the same goal: canceling your jump charge so you can boost and keep your boost duration. If you release your jump charge in the 14 frames of control lock after you speed up from a dash panel, the jump charge will be canceled (without doing your jump), and you can boost chain again with the additional speed from the dash panel. With a JCBCBC, the concept is similar, you cancel your jump charge in the same way you would do a JCBCDPC, but instead of canceling the jump charge from a dash panel, you cancel the jump charge from bonking into a wall. This act is typically referred to as a "bonk dash".
And that is everything you need to know to boost chain! As always, the best way to learn is to practice and experiment with yourself to find out the best timings for boost chain, and when you should (or shouldn't) boost chain.