Create stacked barplot where each stack is scaled to sum to 100%

Here's a solution using that ggplot package (version 3.x) in addition to what you've gotten so far.

We use the position argument of geom_bar set to position = "fill". You may also use position = position_fill() if you want to use the arguments of position_fill() (vjust and reverse).

Note that your data is in a 'wide' format, whereas ggplot2 requires it to be in a 'long' format. Thus, we first need to gather the data.

library(ggplot2)
library(dplyr)
library(tidyr)

dat <- read.table(text = "    ONE TWO THREE
1   23  234 324
2   34  534 12
3   56  324 124
4   34  234 124
5   123 534 654",sep = "",header = TRUE)

# Add an id variable for the filled regions and reshape
datm <- dat %>% 
  mutate(ind = factor(row_number())) %>%  
  gather(variable, value, -ind)

ggplot(datm, aes(x = variable, y = value, fill = ind)) + 
    geom_bar(position = "fill",stat = "identity") +
    # or:
    # geom_bar(position = position_fill(), stat = "identity") 
    scale_y_continuous(labels = scales::percent_format())

Chris Beeley is rigth, you only need the proportions by column. Using your data is:

 your_matrix<-( 
               rbind(
                       c(23,234,324), 
                       c(34,534,12), 
                       c(56,324,124), 
                       c(34,234,124),
                       c(123,534,654)
                    )
                )

 barplot(prop.table(your_matrix, 2) )

Gives: