Yeah, if you don't have a table saw, then the trick is gonna be getting a perfect kerf cut with a handsaw , but if you have a table saw (typical 1/8 standard kerf or 3/32 thin kerf blade) you can get kerf width strips if you have a wide enough board to rip it in half, then nudge fence a bit narrower and rip both pieces to exactly the same width, then without moving the fence, butt up both pieces side by side (so one piece will be getting cut) and cut a kerf in the outer piece but not all the way through - leave about a half inch uncut, then use handsaw to trim back the "wedge" left by the saw blade to get a semi-flat pushing surface. Take that piece and set the long smooth side against fence, use the notched side to push your filler strip wood through for as many filler strips as you need - since the fence hasnt moved the whole piece should be exactly the cut width less a kerf width, so using it to push another piece through, you get a kerf-width piece on each cut (easier to show than explain). Of course, it does require boards of enough width to be able to do that trick while keeping hands safely away from blade (and guards in place since the thin strips trapped between the push board and the blade can of course catch at the back of blade and come flying back at you)
depending on the size of your pieces, might also be possible to cut your kerfs using a router with a straight bit (and clamping a guide fence to make your angle cuts)
If you have a planer, you can use double stick tape to stick a strip to a carrier board after you get a kerf cut (assuming kerf is nice and parallel) and plane it down to the exact kerf thickness you need so you get a nice tight-fitting filler strip...
