Only Goku has mastered Kaioken, using up to x20 but never combining it with Super Saiyan. Combining Kaioken with SSJ is risky due to the emotional stress of SSJ affecting ki control.

It’s actually something we see appear again in the 2015 instalment, Dragon Ball Super, leading to a slightly different variation of Goku’s Kaioken in the film. Super Saiyan ...

Goku's Super Saiyan Blue with Kaioken combines two techniques, greatly increasing his power but straining his energy and stamina levels. Vegeta's Super Saiyan Blue Evolved is a new transformation ...

Perhaps Goku felt that using Kaioken while in his Super Saiyan Blue form simply wouldn’t be able to overpower Broly fast enough for him to not overcome it.

As you can see in the video below, Goku will be putting on a bright red and blue color show when he goes from Super Saiyan Blue to Kaio-Ken 20x while in that form!