Welcome to the forum! Several thoughts:
1. This "Travel Tips Section" subforum generally has more to do with transportation and accommodations, etc., than about preferred flies. For questions about flies in Montana, you might want to instead post your question on the "Rocky Mountain Range" subforum.
2. That said , Montana is a big state with many different kinds of waters: freestone, tailwater, spring creeks, still water, etc. There are so many variables that you need to provide more specific info about where and when you are planning to fish. Even in June it can vary - -you might, or might not, be there during a salmonfly hatch.
3. When you get to the rocky Mountain subforum, you will find this pinned thread: https://www.theflyfishingforum.com/...the-rocky-mountain-region.365227/#post-773248
4. My guess is that 50% of the responses to your question will be "call a local fly shop for the areas you plan to fish, and also support them by buying some flies while you are there".