Trjtdtk

I'd like to align the elements of the PlotLegend in a single horizontal row beneath the TimelinePlot, as there is plenty of room for that (especially when I adjust the Size to be large). Instead the internal algorithms pack the PlotLegends into three rows in this case.

How to fix that?

TimelinePlot[
 "Hokusai" -> Interval["1760", "1849"]
 
 ,
 PlotStyle -> Red, Orange, Darker[Yellow], Green, Blue, Purple, 
 Black,
 PlotLegends -> 
 Placed[Text[Style["Italian", 16, Italic, FontFamily -> "Times"]],
 Text[Style["French", 16, Italic, FontFamily -> "Times"]],
 Text[Style["American", 16, Italic, FontFamily -> "Times"]],
 Text[Style["British", 16, Italic, FontFamily -> "Times"]],
 Text[Style["Flemish", 16, Italic, FontFamily -> "Times"]],
 Text[Style["Spanish", 16, Italic, FontFamily -> "Times"]],
 Text[Style["Japanese", 16, Italic, FontFamily -> "Times"]], 
 Below],
 AspectRatio -> 1/2,
 PlotLayout -> "Packed",
 Background -> LightGray,
 ImageSize -> 600,
 AxesOrigin -> Center]

You can do this by Legendeding the plot itself and then using LegendLayout:

tlp = TimelinePlot["Thomas Gainsborough" -> 
 Interval["1727", "1788"], 
 PlotStyle -> Red, Orange, Darker[Yellow], Green, Blue, Purple, 
 Black, AspectRatio -> 1/2, PlotLayout -> "Packed", 
 Background -> LightGray, ImageSize -> 600, AxesOrigin -> Center]

Now we add our legend. Note the LegendLayout function:

Legended[tlp,
 Placed[
 LineLegend[Red, Orange, Darker[Yellow], Green, Blue, Purple, Black,
 "Italian", 
 "French", "American", "British", "Flemish", "Spanish", 
 "Japanese", 
 LabelStyle -> 16, Italic, FontFamily -> "Times",
 LegendLayout -> (Row[Row[#, Spacer[1]] & /@ #, Spacer[7]] &), 
 LegendMargins -> 0], Below]]

Resulting in:

I'm sure there's a more elegant way to do this than creating nested Rows, but I'm afraid I don't have the time to have a look.

Just a slightly different take for readability avoiding Slot, using Riffle for the Spacers and constructing the graphics with centralized components (e.g. using With):

With[
 data = 
 "Thomas Gainsborough" -> Interval["1727", "1788"]
 , colors = Red, Orange, Darker[Yellow], Green, Blue, Purple, Black 
 , styleFunc = Function[ text, 
 Style[ text, 16, Italic, FontFamily -> "Times"]
 ]
 , labels = "Italian", "French", "American", "British", "Flemish", "Spanish", "Japanese" 
 , layoutFunc = Function[ pairs, (* pairs = col1, lbl1, ... *)
 pairs // RightComposition[
 Flatten
 , Curry[Riffle][Spacer[2] (* after color *), Spacer[10] (* between labels *) ] 
 , Row
 ]
 ]
 
 ,
 TimelinePlot[ data
 , PlotStyle -> colors
 , AxesOrigin -> Center
 , AspectRatio -> 1/2
 , PlotLegends -> Curry[Placed][Bottom] @ LineLegend[
 colors,
 styleFunc /@ labels
 , LegendLayout -> layoutFunc
 , LegendMargins -> 0
 ] 
 , PlotLayout -> "Packed"
 , Background -> LightGray
 , ImageSize -> 600
 ]
]

Per this answer, you can use the option LegendLayout -> "Row", 1.

data = "Piet Mondrian" -> 
 Interval["1872", "1944"];

labels = Text[
 Style["Italian", 16, Italic, FontFamily -> "Times"]], 
 Text[Style["French", 16, Italic, FontFamily -> "Times"]], 
 Text[Style["American", 16, Italic, FontFamily -> "Times"]], 
 Text[Style["British", 16, Italic, FontFamily -> "Times"]], 
 Text[Style["Flemish", 16, Italic, FontFamily -> "Times"]], 
 Text[Style["Spanish", 16, Italic, FontFamily -> "Times"]], 
 Text[Style["Japanese", 16, Italic, FontFamily -> "Times"]];

TimelinePlot[data, 
 PlotStyle -> Red, Orange, Darker[Yellow], Green, Blue, Purple, Black, 
 PlotLegends -> Placed[LineLegend[labels, LegendLayout -> "Row", 1], Below], 
 AspectRatio -> 1/2, 
 PlotLayout -> "Packed", 
 Background -> LightGray, 
 ImageSize -> 600, 
 AxesOrigin -> Center
]