Jamieson, Fausset and Brown on Philippians 1:19

19. turn to my salvation--"turn out to me for, (or unto) salvation." This proclamation of Christ every way will turn out to my spiritual good. Christ, whose interests are my interests, being glorified thereby; and so the coming of His kingdom being furthered, which, when it does come, will bring completed "SALVATION" (He 9:28) to me and all whose "earnest expectation" (Php 1:20) is that Christ may be magnified in them. So far is their preaching from causing me, as they thought, tribulation in my bonds (Php 1:16). Paul plainly quotes and applies to himself the very words of the Septuagint (Job 13:16), "This shall turn out to my salvation," which belong to all God's people of every age, in their tribulation (compare Job 13:15).

through your prayer and the supply--The Greek intimately joins the two nouns together, by having but one preposition and one article: "Through your prayer and (the consequent) supply of the Spirit of Jesus Christ (obtained for me through your prayer)."