I'm a little embarrassed to offer this as advice, but what has worked for me with my 17month old was to develop an association between the buggy and a little snack
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It's not a bribe as such, and certainly not to 'reward' a tantrum, it's more preemptive, and around the time he would require a snack anyway. I think they tire out pretty quickly and need lots of little snacks at this age anyway, as they're burning so much energy.
So for example, I'd take him out in the buggy from home to somewhere he could walk fairly freely, tire him out a little then at the point when I would need him back in say would you like something to eat now and a little rest? then kind of say let's get you back in the buggy so you can have it. Usually something like a rice cake to keep him occupied while you get on with what you need to. I now find that he gets in of his own accord now when he's tired and doesn't always require the incentive, it was more breaking the negative association he had with the buggy iyswim. Also I think it helps if he knows what's coming.
When he is in full thrash, say if I try and take him away from something interesting, I usually stop trying to put him in the buggy at that point, as I know it isn't going to end well, and just hold him or try and distract him (if possible) until it passes, then when he is calm, firmly carry on strapping him in. I find he is usually is more pliable on a second try, having used up his energy on the first one!
I know how hard it is when they do the flailing thing, my ds is a whopper and sometimes I find it hard to restrain him. Try not to worry about other people, it is what toddlers do from time to time, they are so frustrated with their limitations, and it will have happened to most at some stage!