The Artley Wilkins flute is a silver flute (not plated like a student model). However, "solid silver" flutes are not 100% silver. At best, if it's sterling silver, that is 92.5% silver. Usually (but not always), sterling silver flutes are stamped "Sterling Silver". I'm not sure about the silver % in the Wilkins, but it may be coin silver which at best may be 90% silver.
So lets calculate the estimated salvage value of the flute. On average, a flute weighs about 1 pound or 16 ounces. Of that 16 ounces, there are steel rods (key shafts which may weigh about 2-3 ounces, the head cork probably weighs an ounce or so, and the pads add another ounce. So the remaining parts of the flute which are silver probably weigh a total of 16 - 3 -1 - 1= 11 or maybe 12 ounces. Let's assume that the Wilkins is coin silver (since it is not marked as sterling). 12 x 0.9 = 10.8 ounces of pure silver. Let's round that up to 11 ounces. Today, the selling price of silver is about $17 per ounce. A salvage firm will not pay that much because they have to separate out the non-silver parts and they have to make a profit, so I would guess they would probably pay only about half the selling price of silver, so lets say that comes to $8.50 per ounce. 11 ounces X $8.50 = $93.50.
So, you could get maybe a $100 or so salvage value from the silver, but if you don't want to try to sell it as a flute, rather than scrapping it for salvage value, why not consider donating it to a charitable organization who could themselves sell it in thrift store or perhaps give to a needy family with a child who wants to play flute? Then, you could take a tax deduction for a donation to a non-profit organization. That would give you a donation value of perhaps $300-$500 based upon eBay market prices. You get something, the non-profit gets something, and perhaps a needy students gets something (a flute). That seems to be a win-win for everyone.
"Never give a flute player a screwdriver."