The following shows how to use plotlyProxyInvoke to call plotlys "extendTraces" JS function to add a datapoint to the plot each second:

library(shiny)
library(plotly)

ui <- fluidPage(
  plotlyOutput("linePlot")
)

server <- function(input, output, session) {
  
  initial_plot <- plot_ly(
    x = 0,
    y = 0,
    type = 'scatter',
    mode = 'lines'
  )
  
  output$linePlot <- renderPlotly({
    initial_plot
  })
  
  lineProxy <- plotlyProxy("linePlot", session)
  
  xData <- reactiveVal(0)
  yData <- reactiveVal(NULL)
  
  observe({
    invalidateLater(1000)
    isolate(xData(xData()+1))
    yData(runif(n = 1, min = 0, max = 1))
  })
  
  observe({
    plotlyProxyInvoke(lineProxy, "extendTraces", list(x = list(list(xData())), y = list(list(yData()))), list(0))
  })
  
}

shinyApp(ui, server)

Also see my related answer here.

Edit: After the example data was explained.

Due to the fact, that your data source is updated only once every 24h I'd like to simplify things. The following solution re-renders the chart every minute (we have got the time for that) based on the latest data:

library(Quandl)
library(plotly)
library(shiny)

theme_set(theme_minimal())

ui <- fluidPage(
  plotlyOutput("yield_chart"),
  tags$style(type="text/css", "#yield_chart.recalculating { opacity: 1.0;"), # comment out to see the graph recalculating
)

server <- function(input, output, session) {

  treas_yields <- reactive({
    invalidateLater(1000*60) # update every minute
    DF <- Quandl("USTREASURY/YIELD", api_key="123xyz")
    subset(DF, `10 YR` != 0)
  })

  output$yield_chart <- renderPlotly({
    print(paste(Sys.time(), "rendering plotly graph"))
    plot_ly(treas_yields(), x = ~Date, y = ~`10 YR`, name = '10 Yr.', type = 'scatter', mode = 'lines', line=list(color='darkred'))
  })
    
}

shinyApp(ui, server)    

First of all, two remarks on your post :

• it is not reproducible, see here to learn what a reproducible example is and how to make one
• There are already several posts about this. Typing "r shiny plotly output" in any search engine gives several potential solutions (here for example).

To avoid duplicated posts, please consider these two points next time.

Now, here's the answer (using iris data since your example is not reproducible):

library(shiny)
library(plotly)

ui <- fluidPage(
  selectInput("choice", "Choose", choices = names(iris), selected = NULL),
  plotlyOutput("graph")
  )

server <- function(input, output, session){
  
  output$graph <- renderPlotly({
    plot_ly(iris, x = ~get(input$choice), y = ~Sepal.Length, type = 'scatter', mode = 'markers')
  })
}

shinyApp(ui, server)