Pete -
If you are looking for one of those truly large Skagit fish - and yes they do exist - on the fly then it is my opinion that the very best time is the later part of February.

It is this time of the year when those largest males are entering the river. This traveling fish are the most aggressive of the year. However it is also the time of year when you are mostly likely to get shunked - the hatchery fish are all but done (a few kelts) and while the larger males are in entering the river most are several weeks away.

If you are looking for the best fishing with a chance at a "toad" then the CnR season (mid-March to the end of April) is the time to be there. The peak varies depending on the water year but for the feather tosser I would look at mid-April.

Tight lines
S malma