Look at the local streambeds and copy them. Unless you find local black lava streambeds, don't try to make it work in your yard unless you are going for a totally modernistic unnatural look. For a natural look, vary the size of the rocks, with some big ones anchoring the bends and interrupting the "stream", with smaller rocks. This is a good one. https://www.pinterest.com/pin/210754457531720328/ You want to avoid the drainage ditch full of gravel look.

Yes a picture would be much easier. In the picture this is looking up a hill. Its decieving but to the right of the drain is another hill. The tree on the left of the drain has a 4 inch root going under the drain. I need to do something here and because of the slope I can't go much further to the right and can't go deeper without cutting the tree root. Thats why I was wondering if that stretch I could put a pipe in the very bottom for unobstructed water flow, but I have never seen that done and can't find an example online. So that makes me wonder if its a dumb idea. Ideas are appreciated. Thanks.

"is there any evidence that a rock creek bed would be superior to a swale for moving storm-water through the property?" No. Rock mulch might be preferable, though, in situations where grass or groundcover can't grow well. However, this is very few situations. Dry stream beds are usually created because someone wants the appearance of such a structure. Unfortunately, many of them are not well done and don't look good.

Will the bed be used to redirect run-off during rainy times and with snow melt or will it remain dry and just be decorative? If intended to be functional, you want to make sure it is sized appropriately to accommodate the water flow. Typically, dry stream or creek beds are wider than they are deep. And usually by a ratio of 2:1. So a 2-3' wide bed should be 12-18" deep. The rocks you use should be in a range of sizes, just as they would be in a real stream bed. You will need a fair number of large rocks (6-10") as edging along the sides but placed rather randomly. And even a few random larger boulders, especially sited at any curves in the stream bed. For that length and width, you will need 2-3 tons of 1-4" diameter river rock and probably another ton of the larger sized rock (~80-100). The boulders you would purchase by quantity rather than weight.....as many as you need. Make sure you lay landscape fabric along your stream trench (anchor it firmly in place with the boulders and large edging rocks) and then a 1-2" layer of coarse sand. Then fill with your river rocks, evening them out a bit across the surface. You can use whatever shade tolerant plants you like but generally you want lower growing plants closer to the edges of the steam bed and taller plants at a bit of distance. Hostas come to mind immediately, with perhaps some Japanese forest grass (Hakonechloa) here and there along the edge. Primulas are another possibility if enough moisture in the area. Other plants I would consider are astilbe and columbine for some height but you can really use any combintion of shade tolerant plants you like. Pinterest is good for some inspiration on planting layouts. The bottom line is you want it to look natural. So avoid any rows of plants or too precise placements :-)