How to add logo in upper left and right corner of baposter

Welcome to TeX.SE. You can set a logo on the left of the title by adding eyecatcher=true and then using includegraphics... to add the logo. The logo on the right is also added using includegraphics.... To get logos in the upper left and right of the page, you can apply them on the background using the background macro.

documentclass[landscape,a0paper]{baposter} % Adjust the font scale/size here fontscale=0.285
usepackage{graphicx} % Required for including images
graphicspath{{figures/}} % Directory in which figures are storedhttps://www.overleaf.com/project/5f12e7a80c36e30001056c20
usepackage{amsmath} % For typesetting math
usepackage{amssymb} % Adds new symbols to be used in math mode
usepackage{booktabs} % Top and bottom rules for tables
usepackage{enumitem} % Used to reduce itemize/enumerate spacing
usepackage{palatino} % Use the Palatino font
usepackage[font=small,labelfont=bf]{caption} % Required for specifying captions to tables and figures

usepackage{multicol} % Required for multiple columns
setlength{columnsep}{1.5em} % Slightly increase the space between columns
setlength{columnseprule}{0mm} % No horizontal rule between columns

usepackage{tikz} % Required for flow chart
usetikzlibrary{shapes,arrows} % Tikz libraries required for the flow chart in the template

newcommand{compresslist}{ % Define a command to reduce spacing within itemize/enumerate environments, this is used right after begin{itemize} or begin{enumerate}
setlength{itemsep}{1pt}
setlength{parskip}{0pt}
setlength{parsep}{0pt}
}

definecolor{lightblue}{rgb}{0.145,0.6666,1} % Defines the color used for content box headers
definecolor{green1}{cmyk}{0.2,0.8,0.0,0.2}
definecolor{darkblue}{cmyk}{0.8,0.2,0.0,0.8}
definecolor{darkgreen}{cmyk}{0.8,0,0.0,0.45}
definecolor{lightgreen}{cmyk}{0.8,0,0.0,0.25}

begin{document}
background{
    begin{tikzpicture}[remember picture,overlay]%
    node[anchor=north west] at (current page.north west) {includegraphics[height=2em, width = 2em]{example-image-a}};
    node[anchor=north east] at (current page.north east) {includegraphics[height=2em, width = 2em]{example-image-a}};
    end{tikzpicture}
}
begin{poster}
{
headerborder=open, % Adds a border around the header of content boxes
colspacing=1em, % Column spacing
bgColorOne=white, % Background color for the gradient on the left side of the poster
bgColorTwo=white, % Background color for the gradient on the right side of the poster
borderColor=lightblue, % Border color
headerColorOne=lightgreen, % Background color for the header in the content boxes (left side)
headerColorTwo=lightgreen, % Background color for the header in the content boxes (right side)
headerFontColor=white, % Text color for the header text in the content boxes
boxColorOne=white, % Background color of the content boxes
textborder=roundedleft, % Format of the border around content boxes, can be: none, bars, coils, triangles, rectangle, rounded, roundedsmall, roundedright or faded
eyecatcher=true, % Set to false for ignoring the left logo in the title and move the title left
headerheight=0.3textheight, % Height of the header
headershape=roundedright, % Specify the rounded corner in the content box headers, can be: rectangle, small-rounded, roundedright, roundedleft or rounded
headerfont=Largebftextsf, % Large, bold and sans serif font in the headers of content boxes
%textfont={setlength{parindent}{1.5em}}, % Uncomment for paragraph indentation
linewidth=2pt, % Width of the border lines around content boxes
background=user %<-- added
}
%----------------------------------------------------------------------------------------
%   TITLE SECTION
%----------------------------------------------------------------------------------------
{includegraphics[height=2em, width = 2em]{example-image-a}} %<-- eyecatcher
% {includegraphics[height=1.5 em, width = 2.5 em]{logo.png}} % First university/lab logo on the left
{bfseriessffamilytextcolor{darkblue}{A very long Title}} % Poster title
%{textsf{}}vspace{0.1em}{}
% Author names and institution
{Authors}
{includegraphics[height=2em, width = 2em]{example-image-a}}
 % Second university/lab logo on the right

%----------------------------------------------------------------------------------------
%   OBJECTIVES
%----------------------------------------------------------------------------------------

begin{posterbox}[name=1,column=0,row=0, span = 2]{Introduction}
end{posterbox}

end{poster}
end{document}