The Beaverkill is a very fertile stream, rich in insect life, and which generally tend to be small in size, #14 - 22. I usually recommend the wool body kebari for subsurface fishing , and the simplified thread body & rooster hackle kebari for drys. Actually, you can get by with a simple selection since tenkara techniques are so effective in luring trout.
Most hatches occur in the spring months through June, but Cinnamon & Spotted Sedges may be active during your trip. For subsurface fishing Skye's Bracken or leprechaun in size #16 works well for these. For dry flies, a light olive simplified body with brown rooster hackle, again on a #16 hook, tied both bushy and sparse.
Sulfur Mayflies may also be available, and a Pheasant Tail kebari, both floating and sinking in size #16 will be useful. The floating pattern is not available in the store, but I do tie them for regular customers.
The Golden Drakes & Slate Drakes like slower water and are usually best fished on bottom. The Skyes Killer Kebari soft hackle should suffice in size #14 as an emerger, also an Eastern Killer bug might be useful at depth.
The Gray Wing Yellow Quill & Cream Cahill can be covered with the Amano, the Skyes Buttermilk for an emerger, or Eastern Killer Bug for a nymph imitation.
Ants & Beetles will also be important for you. The Akiyamago Hyashi Black simplified works as a beetle near logs of the bank & overhanging vegetation. I recommend some ant imitations as well.
You should see the very beginning of the Blue Wing Olive hatch which usually starts the 2nd week of July. The Pheasant Tail kebari is again useful with these in Size #16. The Little Sister caddis is also imitated by the Skyes Bracken.
Midges are good all of the season and a size #18 black bead head should be helpful. Minnows & sculpins are best imitated by the olive or gray Killer Buggers.
So, this should begin to give a sense that a selection of subsurface flies in 14-16, and simplified kebari, same sizes in Black, brown, tan, olive and gray will get you by using tenkara techniques. I find the Killer Bugs are the most useful for nymph fishing, Skye's for wet fly techniques, and the Simplified rooster hackles for hatching insects.