This shows how to move the image to the lower right corner. It shrinks the image to fit the margin.
\documentclass[a4paper, twoside, 12pt, hidelinks, final]{article}
\usepackage[top=1in, bottom=1in, left=0.75in, right=0.75in, headheight=35.4pt, footskip=35.4pt]{geometry}
\usepackage{eso-pic} % https://ctan.org/pkg/eso-pic?lang=en
\usepackage{graphicx} % https://ctan.org/pkg/graphicx?lang=en
\newsavebox{\logo}
\savebox{\logo}{\includegraphics[width=0.75in]{example-image}}% do once, then copy
\AddToShipoutPictureFG*{\put(\LenToUnit{\dimexpr \paperwidth-0.75in},0){\usebox\logo}}
\begin{document}
\clearpage\mbox{}\clearpage
\end{document}
This solution sets the margin to match the image size.
\documentclass[a4paper, twoside, 12pt, hidelinks, final]{article}
\usepackage{graphicx} % https://ctan.org/pkg/graphicx?lang=en
\newsavebox{\logo}
\savebox{\logo}{\includegraphics[scale=0.3]{example-image}}% do once, then copy
\usepackage[top=1in, bottom=1in, left=\wd\logo, right=\wd\logo, headheight=35.4pt, footskip=35.4pt]{geometry}
\usepackage{eso-pic} % https://ctan.org/pkg/eso-pic?lang=en
\AddToShipoutPictureFG*{\put(\LenToUnit{\dimexpr \paperwidth-\wd\logo},0){\usebox\logo}}
\begin{document}
\clearpage\mbox{}\clearpage
\end{document}
This solution uses flowfram. I added an \intextsep gap above and a \columnsep gap beside the logo. I also added a \dp\strutbox gap between the two flow frames to try to emulate \baselineskip.
In this case, the first break occurs between two paragraphs, but you still need to add a \framebreak to prevent the next paragraph from being formatted at the wrong width. To manually insert \framebreak and \nopar, run it without and the appropriate location should be obvious.
\documentclass[a4paper, twoside, 12pt, hidelinks, final]{article}
\usepackage[top=1in, bottom=1in, left=0.75in, right=0.75in, headheight=35.4pt, footskip=35.4pt]{geometry}
\usepackage{graphicx} % https://ctan.org/pkg/graphicx?lang=en
\usepackage{flowfram}
\usepackage{lipsum}% MWE only
%framebreak within a paragraph
\newcommand{\nopar}{\parfillskip=0pt\framebreak\parfillskip=0pt plus1fil\noindent}
\newsavebox{\logo}
\savebox{\logo}{\includegraphics[scale=0.5]{example-image}}% get width and height
\newstaticframe{\wd\logo}{\ht\logo}{\dimexpr \paperwidth-0.75in-\wd\logo}{-1in}
\setstaticcontents{1}{\usebox\logo}
\newflowframe{\textwidth}{\dimexpr \textheight+1in-\ht\logo-\intextsep}{0pt}{\dimexpr \ht\logo-1in+\intextsep}
\newflowframe{\dimexpr \textwidth+0.75in-\wd\logo-\columnsep}{\dimexpr \ht\logo-1in+\intextsep-\dp\strutbox}{0pt}{0pt}
\begin{document}
\lipsum[1-6]\framebreak
Sed commodo posuere pede. Mauris ut est. Ut quis purus. Sed ac odio. Sed vehicula
hendrerit sem. Duis non odio. Morbi ut dui. Sed accumsan risus eget odio. In hac habitasse
platea dictumst. Pellentesque non elit. Fusce sed justo eu urna porta tincidunt. Mauris felis odio,\nopar
sollicitudin sed, volutpat a, ornare ac, erat. Morbi quis dolor. Donec pellentesque, erat ac sagittis
semper, nunc dui lobortis purus, quis congue purus metus ultricies tellus. Proin et quam. Class
aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos hymenaeos. Praesent
sapien turpis, fermentum vel, eleifend faucibus, vehicula eu, lacus.
\lipsum[8-10]
\end{document}
eso-picpackage. – Bernard Aug 02 '19 at 12:47