Do soldiers of the Salvation Army have an official salute?

Yes, they do. The salute involves raising the right hand above shoulder-length with the index finger pointing upwards.
https://en.wikipedia.org/wiki/The_Salvation_Army#Salute

The Salvation Army salute is given by pointing upwards with the index finger of the right hand. It signifies recognition of a fellow-citizen of, and a traveller to, heaven, and a pledge to do everything possible to get others to heaven also. On appropriate occasions the recognized military salute of the country concerned is used but is not otherwise in order between Salvationists. For a brief period, at the instigation of George Scott-Railton, the sign language equivalent for the letter S was exchanged when Salvationists met.

Photo:

http://www1.salvationarmy.org.uk/uki/www_uki_ihc.nsf/stc-vw-sublinks/8B36901CFBFAF7468025707B003CB1A4?openDocument