when a lot of people first learn the triangle, they think that they are just not flexible enough to do it. the key in most positions is proper hip position. i view flexibility in BJJ as a tool that will make everything flow better and easier to understand, but everybody with shit flexibility still has the potential to pull off the moves. basically, the less flexibility you have, the more correct you have to do the move.
i do prasara yoga mainly. you can see some vids on youtube of people doing a prasara yoga demo and then doing the motions on people to show the transfer to grappling. the spider monkey flow will help develop flexibility in passing. the tumbleweed flow will help develop flexibility in inverted guard. the pigeon flow will help you transfer your weight between feet for taking shots and what not. etc.
i find that doing gymnastic motions never makes me stiff. front levers will also teach you how to keep your elbows in close and tight. i don't really feel that squatting makes you stiff, it's just how much of it you do. a thing to keep in mind is that you have the most potential energy when you are in a ball/fetal. therefore every single one of your squats should tea-bag the floor. if you're not digging as low as possible, then i feel like you're going to set yourself up to get stiffer in grappling.
deck squats are good since they require you to fold into a ball. if you want to use them instead of squatting, then roll and jump to something high up or do them one legged. as a warm-up i love rolling into plow position on one shoulder, then rolling forward through butteryfly into a semi-lunge. i could explain that more, but you probably know what i'm talking about.