You can find the second point given a line, starting point, and distance using the GeometryService. The method you use depends on whether you want absolute distance from the starting point (as the crow flies), or traveling distance.
Absolute Distance (as the crow flies)
- Create a Buffer around the starting point that's the distance you want.
- Convert the edge of the buffer polygon into a polyline
- Intersect the line in question with the buffer edge polyline to get the end point
- Break up a line by its vertices into individual line segments.
- Use a Lengths calculator to find the length of each line segment
- Starting from the beginning, deduct the length of each line segment from the length you want, until there's more length in a segment than in the remaining total.
- Break the last segment into by the fractional distance remaining to make the entire line the length you require.
- Find the point on the end of that line. That's your destination.
Here's a link to a jsFiddle I put together for the travelling distance calculator. you draw a line, and it cuts it off at the 5 mile mark. See it here.