Converting my Raleigh Equipe to a single speed: Can I use a conversion kit?
No, you have a freewheel and the conversion kit you have bough is for a freehub. The freehub you have linked to will not fit your freewheel.   

I don't know if you can get freewheel kits with spacing.  Most freewheel kits I have seen have the cog close the hub flange - the chain line would be wrong on your wheel.