Tested this issue on Windows 10 on the reported version 69.0.3497.81 and the latest Canary 71.0.3554.0 and unable to reproduce the issue by following the below steps.

1. Launched Chrome and added few themes like 'Flying Paint', 'Alloy'.
2. Entered URL in the omnibox and couldn't observe any artifacts.
3. Launched a new-Incognito window and can see the '+' button placed correctly.
Attached is the screen cast for reference.

As we are unable to access the Feedback URLs given in Comment #0, routing to inhouse team to check just in case the feedback URLs have any additional info. available.
Hence adding 'TE-NeedsTriageFromHYD' label.

Thanks..

+ screen cast

Deleted: 884358.mp4 1.2 MB

	884358.mp4 1.2 MB View Download

This doesn't look omnibox-specific.

Possibly related issue: https://crbug.com/881834

In comment 0:

* First screenshot is due to the user's theme.  The theme has various lines in it, and the heights and alignment of elements changed.  The theme author will need to update.
* Second screenshot is a Chrome bug that is now fixed.
* Third screenshot looks like maybe a compositor issue (tile seams?), possibly with high DPI.  I'd consider filing that separately.  Would be good to find a repro case.

Sending to kylixrd@ for initial routing.

Theme tiling issue over to Ryan.

***Mass UI Triage ***

Unable to reproduce the issue on Windows 10 with chrome #72.0.3615.0 as per steps mentioned in the comment #4

Mass-unassigning bugs from rameier@.