Super Saiyan Blue Kaioken is an amalgamation form utilized by Goku during his battle against the legendary assassin Hit. First Goku evolves into his Super Saiyan Blue state of being. After which he performs his Kaioken technique while under the SSB form. The resulting combination creates a unique dual aura. With an outer shell of dark scarlet and the other aura inside being bright turquoise in hue.
Power and Usage
With this technique Goku gains all of the previous abilities as his antecedent Super Saiyan Blue. Additionally this substantial power gets further increased by the linear boost in stats Kaioken has to offer. Hypothetically Kaioken is also capable of being added onto other forms such as Super Saiyan. However doing that will have no benefit as it'll kill the person immediately afterward. What makes Super Saiyan Blue Kaioken able to be executed as opposed to other conjectural techniques is that SSB is an inherent control of ki and emotion, hence the lack of control SSJ has would make it unsuitable to be integrated with Kaioken.
If one wanted to raise the power of this form even further, they could instead replace the regular Kaioken with higher levels such as Kaioken x 2, Kaioken x 3, etc. to mix in with SSB. The greatest technique he shifted with it resulting in a greater form referred to as "Super Saiyan Blue Kaioken x 10." This state causes the user's hair to dilate into a light cyan to somewhat whitish color. After utilizing these forms Son Goku was able to fight back against Hit during his time freeze. Whether resistance against time based attacks is an innate ability of SSBKK, or if this feat was performed by virtue of Goku's own power is currently unknown.
Despite being the strongest form currently in the saiyan's arsenal, it has also proven to have its considerable shortcomings. For one, due to the lack of mastery in this form, Goku only has a 10% chance of actually achieving it and a 90% chance of getting killed in the process. He also faced a severe inability to use his ki properly in the few days after the fight, virtue of the massive strain the form takes on him. Infirmities such as not being able to fly, lack of strength control and difficulty to focus with Instant Transmission were some conditions Goku had afterwards. Fortunately the affects were not permanent and Goku was able to make a full recovery.