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Let a g and b g be the mass of KCl and that of MgCl₂ respectively.

From Wikipedia :
Molar mass of KCl = 74.5513 g/mol
Molar mass of MgCl₂ = 95.211 g/mol
Molar mass of AgCl = 143.32 g/mol

The conversion of KCl to AgCl :
KCl(aq) + AgNO₃(aq) → AgCl(s) + KNO₃(aq)
No. of moles of KCl = (a g) / (74.5513 g/mol) = (a/74.5513) mol
No. of moles of AgCl formed from KCl = [(a/74.5513) mol] × 1 = (a/74.5513) mol
Mass of AgCl formed from KCl = (143.32 g/mol)(a/74.5513 mol) = 1.9224a g

The conversion of MgCl₂ to AgCl :
MgCl₂(aq) + 2AgNO₃(aq) → 2AgCl(s) + Mg(NO₃)₂(aq)
No. of moles of KCl = (b g) / (95.211 g/mol) = (b/95.211) mol
No. of moles of AgCl formed from MgCl₂ = [(b/95.211) mol] × 2 = (2b/95.211) mol
No. of moles of AgCl formed from MgCl₂ = (143.32 g/mol)(2b/95.211 mol) = 3.0106b g

Mass of the mixture (g):
a + b = 1.2505 ...... [1]

Mass of AgCl form (g):
1.9224a + 3.0106b = 2.5788 ...... [2]

[1]×3.0106:
3.0106a + 3.0106b = 3.7648 ...... [3]

[3] - [2]:
1.0882a = 1.1860
a = 1.0899

Mass of KCl in the mixture = 1.0899 g
Percentage by mass of KCl in the mixture = (1.0899/1.2505) × 100% = 87.157%
Percentage by mass of MgCl₂ in the mixture = 1 - 85.157% = 12.843%