Appending an empty row after every 5 or 10 rows in LaTeX table

The following solution sets up an environment blocktable derived from longtable that provides the desired functionality using LaTeX only.

Implementation notes

First, a few counters are needed:

\newcounter{@tabrow}
\newcounter{@emptyrow}
\newcounter{@modulus}
\newcounter{@default@blocksize}

@tabrow will be incremented every row to determine the current row number while @emptyrow will hold multiples of @modulus (which accordingly is set to the number of rows one block/chunk should contain; to be precise it will be @modulus+1). Last mentioned is set internally through \@setblocksize:

\newcommand{\@setblocksize}[1]{%
  \setcounter{@modulus}{#1}
  \setcounter{@emptyrow}{\the@modulus}
  \stepcounter{@modulus}
}

@default@blocksize holds the global default value that will be given to @modulus if no optional argument is specified (see below: blocktable).

The core macro is \empty@or@void@line which expands to an empty line, i.e. &...&\\, if \the@tabrow is a multiple of \the@modulus and to simply nothing if not:

\def\empty@or@void@line{%
  \ifnum\the@tabrow=\the@emptyrow
    \addtocounter{@emptyrow}{\the@modulus}%
    \@colseps\ltx@LT@tabularcr
  \fi}

It will be added to every occurance of \\ by saying:

\def\LT@tabularcr{\ltx@LT@tabularcr\empty@or@void@line}

As seen, in \empty@or@void@line internally the empty row internally gets constructed via \@colseps\ltx@LT@tabularcr where \ltx@LT@tabularcr is a stored version of \LT@tabularcr and \@colseps contains the right number of &s which is done with the help of longtable's \LT@cols (which holds the number of columns!) by an auxiliary command:

\newcommand\build@colseps{%
  \@tempcnta\@ne
  \loop
    \advance\@tempcnta by 1
    \g@addto@macro\@colseps{&}
  \ifnum\@tempcnta<\the\LT@cols\repeat
}

The core functionality is applied to a new environment blocktable based on longtable:

\newenvironment{blocktable}[2][\the@default@blocksize]
  {\@setblocksize{#1}\build@colseps\longtable{@{\stepcounter{@tabrow}}#2}}
  {\endlongtable \gdef\@colseps{} \setcounter{@tabrow}{0}}

which assembles all the work done before. It also cleans up the @tabrow count and \@colseps macro -- which was also allocated empty beforehand.

To make sure that the blocking/chunking begins at the right row the following lines conclude the solution code:

\g@addto@macro\endfirsthead{\setcounter{@tabrow}{1}}
\g@addto@macro\endhead{\setcounter{@tabrow}{1}}
\g@addto@macro\endfoot{\setcounter{@tabrow}{1}}
\g@addto@macro\endlastfoot{\setcounter{@tabrow}{1}}

Example

Figure

Before the complete code here is an example pic produced using the default chunk size of 5:

Complete code

\documentclass{article}
\usepackage{booktabs}
\usepackage{longtable,array}

\makeatletter

\newcounter{@tabrow}
\newcounter{@emptyrow}
\newcounter{@modulus}
\newcounter{@default@blocksize}
\setcounter{@default@blocksize}{5}
\def\@colseps{}

\let\ltx@LT@tabularcr=\LT@tabularcr

\def\empty@or@void@line{%
  \ifnum\the@tabrow=\the@emptyrow
    \addtocounter{@emptyrow}{\the@modulus}%
    \@colseps\ltx@LT@tabularcr
  \fi}
\def\LT@tabularcr{\ltx@LT@tabularcr\empty@or@void@line}
\newenvironment{blocktable}[2][\the@default@blocksize]
  {\@setblocksize{#1}\build@colseps\longtable{@{\stepcounter{@tabrow}}#2}}
  {\endlongtable \gdef\@colseps{} \setcounter{@tabrow}{0}}
\newcommand\build@colseps{%
  \@tempcnta\@ne
  \loop
    \advance\@tempcnta by 1
    \g@addto@macro\@colseps{&}
  \ifnum\@tempcnta<\the\LT@cols\repeat
}
\newcommand{\@setblocksize}[1]{%
  \setcounter{@modulus}{#1}
  \setcounter{@emptyrow}{\the@modulus}
  \stepcounter{@modulus}
}
\newcommand{\defaultBTblocksize}[1]{\setcounter{@default@blocksize}{#1}}
\g@addto@macro\endfirsthead{\setcounter{@tabrow}{1}}
\g@addto@macro\endhead{\setcounter{@tabrow}{1}}
\g@addto@macro\endfoot{\setcounter{@tabrow}{1}}
\g@addto@macro\endlastfoot{\setcounter{@tabrow}{1}}

\makeatother

%\defaultBTblocksize{10}

\begin{document}
\listoftables

\begin{blocktable}{ccc}
  \caption{Boring example table}\\
  \toprule
  \textbf{col1} & \textbf{col2} & \textbf{col3}\\
  \midrule
  \endfirsthead
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  foo & bar & baz\\
  \bottomrule
\end{blocktable}
\end{document}

Remarks

1. I don't use knitr and therefore I did not test the solution with a table generated from an external data file like in the OP's mwe, but it should work without any problems when you declare tabular.environment = 'blocktable'.
2. When inserting an actual blank line there is the caveat that material inserted by @{...} also affects the lines left out (which isn't desiderable in my eyes) and the row numbering is just wrong and tricks are needed. #
3. To not overload this answer I packaged an alternative solution merged with the old one into a github repository: https://github.com/giannotr/blocktable (as a package called blocktable. This isn't an official package and it's neither properly documented nor tested. You get the original solution by chosing the 'emptyline' option).

Since you are using knitr, the simplest thing is to add \\ every tenth row using add.to.row parameter of print.xtable.

This is a very rough code; in the general case you need also to check that MatrixData has more than 10 rows.

\documentclass{article} 
\usepackage{longtable}

\begin{document}

\listoftables

<< label=LongTable, results='asis', echo = FALSE >>=
library(xtable)
set.seed(12345)
MatrixData <- matrix(rnorm(1000), ncol = 10)

caption <- paste("\\hline  \\endfirsthead"  ,                          # First caption
                                "\\caption[]{Example of longtable spanning several pages} \\label{tab:MatrixData} \\\\ \\hline", # Additional captions
                                paste("&", 1:ncol(MatrixData),collapse=" "),                              # Column names
                                "\\\\ \\hline ",
                                "\\endhead", 
                                "\\hline \\multicolumn{11}{r}{\\textit{Continued}} \\                    
                                 \\endfoot
                                 \\endlastfoot",collapse=" ")
positions <- seq(from=10, to=dim(MatrixData)[1], by=10)
print(
  xtable(
      x = MatrixData
    , caption = "Example of longtable spanning several pages"
    #, label = "tab:MatrixData"
    , align = c("l|", rep("r", ncol(MatrixData)))
    , digits = c(rep(3, ncol(MatrixData)+1))
  )

  , table.placement = "H"
  , caption.placement = "top"
  , include.rownames = TRUE
  , include.colnames = TRUE
  , size = "small"
  , tabular.environment = 'longtable'
  , floating = FALSE
  , add.to.row = 
      list(pos = as.list(c(0,positions)),
             command = c(caption,rep("\\\\",length(positions)))))

@

 \end{document}