I've been fishing Burke Lake for about 20 years. In that time I've caught 1 tiger muskie by accident while fishing for bass with conventional spinning tackle. It was about 10-12 pounds and a freak occurrence, and that includes years of trying to catch one on live bait, spoons, and giant spinners. I'd imagine getting one on the fly would be even more difficult.
That being said, Burke Lake usually comes in as one of the better largemouth bass lakes in Virginia based on the VDGIF electro-fishing surveys, along with the Occoquan Res. Unfortunately it is also one of the most pressured lakes because of its easy boat access and location relative to DC. The fish population there is wily and smart, but robust and healthy. Definitely worth a trip, and it's small enough that I fish it in a kayak throughout the year.
There is an island in the middle of the lake, I like to fish both shorelines to the east of it focusing on points with weed cover, and work up in the northeast corner of the lake as well. If you have sonar all the better, they used to dump Christmas trees into the lake to create artificial cover for fish as well.