No need to make reservations with the Museumkaart. Buy the card at one of the smaller museums that are covered (you can see the complete list online of all museums and historic canal homes that are included and plan to stop at whatever one interests you first).
As for Anne Frank House, It's open fairly late. I was there this past May, had purchased my card at the Tassen Museum Hendrikje earlier in the day and around 6PM went to the Anne Frank House. No line, no waiting, no reservation. Now other times of day, it can be very busy at the Anne Frank House. I walked by there several times since I was staying in the area and mid morning and early afternoon there can definitely be a wait to get in, so if you can plan to go just before opening, or hold off for an evening visit, you may significantly reduce the problem of getting inside quickly. At 6PM, I walked right in and showed my card, got my ticket and went over to the security area for a quick check of my handbag. Other museums (like the Stedelijk) have Museumkaart kiosk machines. You swipe your card, your ticket pops out of the machine and you go straight to the security area where they will take the ticket from you and let you right in.
The Rijksmuseum was one that was hit or miss. I went there a number of times over a 2 week visit as Museumkaart lets you visit as often as you want over the course of a year. Some security guards had no problem if you flashed your Museumkaart and they would let you skip the long entrance line just to get into the building (once inside, there is another line to purchase a ticket if you don't have a Museumkaart - this is the line you can skip completely - just show your card to one of the security guards standing outside the main galleries entrance who will scan it). Others guards outside weren't having it and would make everyone get in the entrance line. So if you go early (or late), you won't have to wait as long outside.
The Van Gogh Museum is open late on Fridays, so if your visit covers a Friday, you might want to put off visiting there until the evening. Again, I showed up at the Van Gogh on 2 separate Fridays right after the Rijksmuseum had closed for the day and my Museumkaart let me go straight inside and avoid the line (once inside, there is a security checkpoint that you have to go through, but it moves pretty quickly).