Can the word 'fluently' be interchanged with 'fluidly' in this sentence, "I see I can't write fluidly either."

Merriam-Webster's Eleventh Collegiate Dictionary (2003) has this entry for fluent:

fluent adj (1585) 1 a : capable of flowing : FLUID b : capable of moving with ease and grace {the fluent body of a dancer} 2 a : capable of using a language easily and accurately {fluent in Spanish} {a fluent writer} b : effortlessly smooth and and flowing : POLISHED {a fluent performance} {spoke in fluent English} c : having or showing mastery in of a subject or skill {fluent in math}

So if you were wondering whether fluently applies only to spoken language (as you might suppose if you considered only the second example after definition 2b above), you needn't worry: The adverbial form of fluent definition 2a comprehends both spoken and written English, as the second example after it illustrates.

As for whether you can use fluidly in your original example, one definition of the adjective fluid in the Eleventh Collegiate is

2 : characterized by or employing a smooth easy style {the ballerina's fluid movements} {fluid recitation of his lines}

Considerable overlap exists between fluent definition 2b and fluid definition 2; and this overlap applies to the adverbs fluently and fluidly as well. An Ngram Viewer chart of "write fluidly" (blue line) versus "write fluently" (red line) for the years 1820 through 2008 indicates that the latter is more common in the publications included in Google Books' database:

But "write fluidly" is by no means uncommon in books published over the past several decades, including such serious works as Julia O'Brien, editor, Oxford Encyclopedia of the Bible and Gender Studies (2014):

Not all texts used in some form of public instruction were copied out by individuals who were able to write fluidly. The commentary on Habakkuk from Qumran was apparently copied out letter by letter.

In short, you can use fluidly or fluently in the sentence “I see I can't write fluidly/fluently either,” and convey much the same meaning either way.