Your shape is already well tileable to a seamless pattern. The only problem is to practically do the tiling. If you want fast results, see the ending of this text.
We reconstruct it with some tiling help. We use no numerical dimensions except a couple of rotations. Also we use as few flashy functions as possible to make this repeatable also in other software.
Gradient fills are not essential for this geometry problem, we use only solid grey fills. Gradients are useful to define just before tiling the big pattern, because their angles would need calculations otherwise.
Draw a rectangle, copy it and rotate 90 degrees. The space between the rectangles is not critical, but align them to the same horizontal bottom line.
Draw a square (=a rectangle holding Shift when you draw), place it between the corners of the rectangles. Have smart quides and snap to points on, no other snaps, then it fits easily. The square is our fitting jig.
Group temporarily the rectangles, make a 180 degrees rotated copy, place it at the bottom of the jig and align horizontally with the original rectangle group.
Ungroup all.Dupligate the jig and place them to the top left corner of our first rectangle.
In this phase it surely is useful to practice a little to make exact placements with the direct selection tool. Smart quides are not allways reliable due the big number of objects. Deselect all. With the direct selection tool drag over a copy of the jig square to select all its anchor nodes. Beware selecting anything else. Now you can drag a corner of the square to its place and it snaps exactly, other corners follow. After deselecting all you can as well select the square with the normal selection tool and then continue with the direct selection tool. Beware: It's far too easy to distort shapes - only forget to select all anchors.
Draw an orange rectangle around the shapes. It must fit with the jig squares and the bottom and right sides of the grey rectangles exactly. You can drag its sides separately, but the result will be a square, if there's no errors.
Remove the jig squares. Ungroup all and make a new group which contains all (=the orange and grey shapes). Rotate the group plus or minus 45 degrees, here the rotation is +45 degrees
Now it's the right place to check, if there's something that anti-nazi enthusiasts are sensitive to notice. Beware! Having certain angles and proportions can destroy your business and it will happen if someone at first has some (whatever) reason to find any damaging evidence against you.
Squeeze the rotated shape vertically as you like.
If you want gradient fills, they are defined most easily before tiling. Ungroup all, Select grey rectangles one by one, drag the gradient directions by eye and group all again. A slight gradient direction error is invisible.
Now it's easily manually tileable. Use the direct selection tool to place the corners exactly. By duplicating a tiled pattern you can easily cover large areas.
There are several approaches how to get rid of the orange shapes.
An effective idea is to define the tileable shape from phase 7 or 8 to be a symbol (=drag to the symbols panel). Tile symbol instaces only. You can edit the symbol to remove the stroke of the orange rectangle. Any edit affects all instances. In the next image the orange stroke is removed (the color only, the frame can be useful later for placements) and grey rectangles are colored
If you do not want to use symbols, you can break the symbol links or tile the elements from phase 7 or 8. If you tile diectly from 7 or 8, finally select one separate orange rectangle, then goto Select > Same > Stroke Color. Now you can delete the orange frames or change them to have no stroke color.
When watching the result, it soon came clear, that you can organize the same primary elements a little differently. You place 4 rectangles inside a square (blue) and make the jigs (red) for the guide frame (orange) by drawing 2 rectangles between the grey rectangles.
This organization makes easy to visually predict the final density of the tiled pattern.
Finally: You can put into a tileable frame anything and the result is easily tileable: