Code for DEM based flow routing in R
Take a look at the RSAGA package on CRAN, or the rgdal package. Many of the GIS methods can be done in R but basically act as a wrapper for saga or gdal. RSAGA is likely your best bet for processing terrains for flow analysis. 

I also know of Dan Moore from UBC who does a lot of work with R and GIS applications, worth taking a look there and certainly those algorithms can be done in R directly.

There is also another post in the GIS forum on using TauDEM in R, worth taking a look as well. TauDEM in R - additional SO post

In general, rseek is an excellent search engine for exactly this type of problem in case you don't find what you are looking for in those links above. 

For actual flood routing, you may be interested in the Height Above Nearest Drainage Model (HAND), which uses the same type of D8 flow accumulation algorithm to build a rapid method for floodplain mapping. Good paper on that some other 1D methods.