Sandeep,
The thrust from the flare tip is a result of the pressure unbalance. The upstream pressure carries the thrust load to the base of the flare, being the elbow or tee where flow is directed to vertical direction upward to flare tip.
I think the thrust loads will add to the loads on the foundation and / or supporting structure.
I think that thrust load is not carried through walls of flare, so there is not concern for the thrust loads causing a buckling failure of the flare stack. Anyway, CAESARII does not perform a buckling failure analysis.
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R Yee