Here's a way that works on my phone (not necessarily "easy" depending on your skill level, but it's a way):
Tested and working on:
Samsung Galaxy S8, Android 9, Outlook for Android 4.0.57 (367)
Method 1 - Embedded image (using Base64 encoding)
----------
Go to
https://www.base64-image.de/
Upload your logo to convert to Base64 format.
Copy the code in to an email on your PC and email to your Android phone.
Copy and paste the code in to Outlook's signature box, and then add the following to the front of it
<img src='
and this at the end of it
'>
The apostrophe's are important that they're the correct one's.
When I tried using the apostrophe on my Windows PC, it didn't like that one, so make sure you type it on the Android phone instead.
Note: once you've setup the sig, Outlook will turn it in to a weird coloured box if you go look directly at the signature box again.
If you need to edit your signature, you'll have to re-paste the code again to get the logo again.
Probably best to keep the email with the Base64 code in your drafts or another folder.
Method 2 - Link to image (using Base64 encoded URL)
----------
Go to
https://mothereff.in/html-entities
Enter in the url to your logo
untick the box "only encode unsafe and non-ASCII characters"
highlight and copy the encoded URL
Email the encoded URL to your android phone
Copy and paste the code in to Outlook's signature box, and then add the following to the front of it
<img src="
and this at the end of it
">
The double-quotes are important that they're the correct one's.
When I tried using the double-quotes on my Windows PC, it didn't like those ones, so make sure you type it on the Android phone instead.
Note: once you've setup the sig, Outlook will turn it in to a weird coloured box if you go look directly at the signature box again.
If you need to edit your signature, you'll have to re-paste the code again to get the logo again.
Probably best to keep the email with the Base64 code in your drafts or another folder.