Finger joints have tapered pins and are used to join boards end to end to make longer paint grade boards. Box joints have square pins and used to make strong corner joints in boxes. I think you want the box joints for your project and not finger joints.
If you cut the box joints in the ends of your boards at 90 degrees to the angled board end this is one of the angles of your tapered box compound joint, and with the board tilted back by the other angle of the compound joint as you cut the box joints you will have the other angle of your compound joint and both boards should fit together. You may need slightly longer box joint pins so the excess can be trimmed off later after the joint is glued together, because the joint is going together at an angle other than 90 deg. the joint overlap of the two boards will result in more of the pin side surfaces being involved in the joint. The bottoms of the cuts in the box joint will be angled back (deeper) as well.
I haven't ever attempted this, but I have cut many box joints for straight sided boxes. I use an Incra I-Box jig and my Unisaw to cut them. I doubt that the I-Box jig could be modified easily to hold a board at the needed angle, but a shop made jig could be designed to do this.
The Kyrmi Mini Fence was available 20 years ago that had backers to hold the boards tilted back at common angles for doing this type of thing on a table saw, but Mr Kyrmi was in his late 80's when I last saw him back then, and he was kind of a one man business at the time, so I doubt that he or his business have survived. His video was on Youtube, but I could not locate it now. It was of very low quality compared to todays videos and provided on a VHS tape with his jig, so they likely pulled it for lack of quality and no use. His jig was very much like a typical box joint jig, but angled backers could be used to tilt the board being cut back at a desired angle while cutting the box joint. The table saw blade then cut the slot at the increasing depth in the board end.
Charley
If you cut the box joints in the ends of your boards at 90 degrees to the angled board end this is one of the angles of your tapered box compound joint, and with the board tilted back by the other angle of the compound joint as you cut the box joints you will have the other angle of your compound joint and both boards should fit together. You may need slightly longer box joint pins so the excess can be trimmed off later after the joint is glued together, because the joint is going together at an angle other than 90 deg. the joint overlap of the two boards will result in more of the pin side surfaces being involved in the joint. The bottoms of the cuts in the box joint will be angled back (deeper) as well.
I haven't ever attempted this, but I have cut many box joints for straight sided boxes. I use an Incra I-Box jig and my Unisaw to cut them. I doubt that the I-Box jig could be modified easily to hold a board at the needed angle, but a shop made jig could be designed to do this.
The Kyrmi Mini Fence was available 20 years ago that had backers to hold the boards tilted back at common angles for doing this type of thing on a table saw, but Mr Kyrmi was in his late 80's when I last saw him back then, and he was kind of a one man business at the time, so I doubt that he or his business have survived. His video was on Youtube, but I could not locate it now. It was of very low quality compared to todays videos and provided on a VHS tape with his jig, so they likely pulled it for lack of quality and no use. His jig was very much like a typical box joint jig, but angled backers could be used to tilt the board being cut back at a desired angle while cutting the box joint. The table saw blade then cut the slot at the increasing depth in the board end.
Charley