IIRC, FindNext ignores the FindFormat, so try a small tweak:
Sub Find_Format_INR()
'
' Find_Format_INR Macro
'
  Dim FirstAddx As String
  Dim FoundIt As Range
  Dim Rng As Range

    Application.FindFormat.NumberFormat = "#,##0.00 ""INR"""
    
    Set Rng = ActiveSheet.UsedRange
    Set FoundIt = Rng.Find(what:="", after:=ActiveCell, LookIn:=xlFormulas, LookAt:= _
                           xlPart, SearchOrder:=xlByRows, SearchDirection:=xlNext, _
                           MatchCase:=False, searchformat:=True)
    If Not FoundIt Is Nothing Then
       FirstAddx = FoundIt.Address
         Do
           FoundIt.Offset(0, 1) = "YES"
           Set FoundIt = Rng.Find(what:="", after:=FoundIt, LookIn:=xlFormulas, LookAt:= _
                           xlPart, SearchOrder:=xlByRows, SearchDirection:=xlNext, _
                           MatchCase:=False, searchformat:=True)
         Loop While FoundIt.Address <> FirstAddx
    End If
    
End Sub