HI @LionelD,
Looks like this is just an HTML rendering issue. If you zoom-in on the table in your browser you will see that the lines all become clearly the same width.
If this is a problem then maybe save the file as a high-resolution PNG file using save_as_image() and then use that.
p.s. Your original code post was missing the border definitions:
library(dplyr)
library(flextable)
library(officer)
big_border = fp_border(color="red", width = 3)
std_border = fp_border(color="blue", width = 1)
iris %>% head(n=4) %>% flextable() %>%
bg(bg = "#00557F", part = "header") %>%
bold(part = "header") %>%
color( color = "white", part = "header") %>%
border_outer(border = big_border, part = "all" ) %>%
border_inner_h( border = std_border, part = "all" ) %>%
border_inner_v( border = std_border, part = "all" ) %>%
autofit() %>%
save_as_html(path = 'ex.html')