  We report $^{31}$P NMR studies of an oriented polycrystalline superconductor
of Ba$_{0.5}$Sr$_{0.5}$Fe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ with $x\sim$ 0.4
($T_\mathrm{c}$ = 29 K) at $T$ = 14$-$325 K and $B_{0}$ = 1 and 5 T. The
$^{31}$P Knight shift $K_{ab}$ at $B_{0}\perp c$ shows a nearly $T$-independent
uniform spin susceptibility above $T_\mathrm{c}$ and a spin singlet decrease
below $T_\mathrm{c}$. The $^{31}$P nuclear spin-lattice relaxation rate
1/$T_{1}$ shows an asymptotic behavior of $a+bT$ ($a$ and $b$ are constants) at
$T >$ 100 K and the minimum at 40 K with an upturn toward $T_\mathrm{c}$. The
$a$ term in 1/$T_{1}$ indicates the presence of two-dimensional
antiferromagnetic spin fluctuations. The negative $\theta$ = $-$15 K of the
Curie-Weiss-type antiferromagnetic spin susceptibility $\chi$($Q$) $\propto$
1/($T$+$\theta$) in the analysis of 1/$T_{1}T$ suggests antiferromagnetic
instability in the superconducting state. Discussions are made from the
self-consistent renormalization (SCR) theory for the spin fluctuations with
interlayer correlation.
